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## Publikationen der Fachgruppe

Liste im Research Information System öffnen

## 2020

Survey on Algorithms for Self-Stabilizing Overlay Networks

M. Feldmann, C. Scheideler, S. Schmid, ACM Computing Surveys (2020)

The maintenance of efficient and robust overlay networks is one of the most fundamental and reoccurring themes in networking. This paper presents a survey of state-of-the-art algorithms to design and repair overlay networks in a distributed manner. In particular, we discuss basic algorithmic primitives to preserve connectivity, review algorithms for the fundamental problem of graph linearization, and then survey self-stabilizing algorithms for metric and scalable topologies. We also identify open problems and avenues for future research.

A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks

J. Castenow, C. Kolb, C. Scheideler, in: Proceedings of the 21st International Conference on Distributed Computing and Networking (ICDCN), ACM, 2020

Time- and Space-Optimal Discrete Clock Synchronization in the Beeping Model

M. Feldmann, A. Khazraei, C. Scheideler, in: Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), ACM, 2020

We consider the clock synchronization problem in the (discrete) beeping model: Given a network of $n$ nodes with each node having a clock value $\delta(v) \in \{0,\ldots T-1\}$, the goal is to synchronize the clock values of all nodes such that they have the same value in any round. As is standard in clock synchronization, we assume \emph{arbitrary activations} for all nodes, i.e., the nodes start their protocol at an arbitrary round (not limited to $\{0,\ldots,T-1\}$). We give an asymptotically optimal algorithm that runs in $4D + \Bigl\lfloor \frac{D}{\lfloor T/4 \rfloor} \Bigr \rfloor \cdot (T \mod 4) = O(D)$ rounds, where $D$ is the diameter of the network. Once all nodes are in sync, they beep at the same round every $T$ rounds. The algorithm drastically improves on the $O(T D)$-bound of \cite{firefly_sync} (where $T$ is required to be at least $4n$, so the bound is no better than $O(nD)$). Our algorithm is very simple as nodes only have to maintain $3$ bits in addition to the $\lceil \log T \rceil$ bits needed to maintain the clock. Furthermore we investigate the complexity of \emph{self-stabilizing} solutions for the clock synchronization problem: We first show lower bounds of $\Omega(\max\{T,n\})$ rounds on the runtime and $\Omega(\log(\max\{T,n\}))$ bits of memory required for any such protocol. Afterwards we present a protocol that runs in $O(\max\{T,n\})$ rounds using at most $O(\log(\max\{T,n\}))$ bits at each node, which is asymptotically optimal with regards to both, runtime and memory requirements.

## 2019

Fast Distributed Algorithms for LP-Type Problems of Low Dimension

K. Hinnenthal, C. Scheideler, M. Struijs, in: 33rd International Symposium on Distributed Computing (DISC 2019), 2019

Always be Two Steps Ahead of Your Enemy - Maintaining a Routable Overlay under Massive Churn with an Almost Up-to-date Adversary

T. Götte, V.R. Vijayalakshmi, C. Scheideler, in: Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19), IEEE, 2019

We investigate the maintenance of overlay networks under massive churn, i.e. nodes joining and leaving the network. We assume an adversary that may churn a constant fraction $\alpha n$ of nodes over the course of $\mathcal{O}(\log n)$ rounds. In particular, the adversary has an almost up-to-date information of the network topology as it can observe an only slightly outdated topology that is at least $2$ rounds old. Other than that, we only have the provably minimal restriction that new nodes can only join the network via nodes that have taken part in the network for at least one round. Our contributions are as follows: First, we show that it is impossible to maintain a connected topology if adversary has up-to-date information about the nodes' connections. Further, we show that our restriction concerning the join is also necessary. As our main result present an algorithm that constructs a new overlay- completely independent of all previous overlays - every $2$ rounds. Furthermore, each node sends and receives only $\mathcal{O}(\log^3 n)$ messages each round. As part of our solution we propose the Linearized DeBruijn Swarm (LDS), a highly churn resistant overlay, which will be maintained by the algorithm. However, our approaches can be transferred to a variety of classical P2P Topologies where nodes are mapped into the $[0,1)$-interval.

Distributed Computation in Node-Capacitated Networks

J. Augustine, M. Ghaffari, R. Gmyr, K. Hinnenthal, F. Kuhn, J. Li, C. Scheideler, in: Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures, ACM, 2019, pp. 69--79

Self-Stabilizing Metric Graphs

R. Gmyr, J. Lefevre, C. Scheideler, Theory Comput. Syst. (2019), 63(2), pp. 177-199

On the Complexity of Local Graph Transformations

C. Scheideler, A. Setzer, in: Proceedings of the 46th International Colloquium on Automata, Languages, and Programming, Dagstuhl Publishing, 2019, pp. 150:1--150:14

We consider the problem of transforming a given graph G_s into a desired graph G_t by applying a minimum number of primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its 1-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary G_s and G_t is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio.

A Loosely Self-stabilizing Protocol for Randomized Congestion Control with Logarithmic Memory

M. Feldmann, T. Götte, C. Scheideler, in: Proceedings of the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Springer, Cham, 2019, pp. 149-164

We consider congestion control in peer-to-peer distributed systems. The problem can be reduced to the following scenario: Consider a set $V$ of $n$ peers (called \emph{clients} in this paper) that want to send messages to a fixed common peer (called \emph{server} in this paper). We assume that each client $v \in V$ sends a message with probability $p(v) \in [0,1)$ and the server has a capacity of $\sigma \in \mathbb{N}$, i.e., it can recieve at most $\sigma$ messages per round and excess messages are dropped. The server can modify these probabilities when clients send messages. Ideally, we wish to converge to a state with $\sum p(v) = \sigma$ and $p(v) = p(w)$ for all $v,w \in V$. We propose a \emph{loosely} self-stabilizing protocol with a slightly relaxed legitimate state. Our protocol lets the system converge from \emph{any} initial state to a state where $\sum p(v) \in \left[\sigma \pm \epsilon\right]$ and $|p(v)-p(w)| \in O(\frac{1}{n})$. This property is then maintained for $\Omega(n^{\mathfrak{c}})$ rounds in expectation. In particular, the initial client probabilities and server variables are not necessarily well-defined, i.e., they may have arbitrary values. Our protocol uses only $O(W + \log n)$ bits of memory where $W$ is length of node identifiers, making it very lightweight. Finally we state a lower bound on the convergence time an see that our protocol performs asymptotically optimal (up to some polylogarithmic factor).

A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks

J. Castenow, C. Kolb, C. Scheideler, in: Proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO), 2019, pp. 345-348

Skeap & Seap: Scalable Distributed Priority Queues for Constant and Arbitrary Priorities

M. Feldmann, C. Scheideler, in: Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), ACM, 2019, pp. 287--296

We propose two protocols for distributed priority queues (denoted by 'heap' for simplicity in this paper) called SKEAP and SEAP. SKEAP realizes a distributed heap for a constant amount of priorities and SEAP one for an arbitrary amount. Both protocols build on an overlay, which induces an aggregation tree on which heap operations are aggregated in batches, ensuring that our protocols scale even for a high rate of incoming requests. As part of SEAP we provide a novel distributed protocol for the k-selection problem that runs in time O(log n) w.h.p. SKEAP guarantees sequential consistency for its heap operations, while SEAP guarantees serializability. SKEAP and SEAP provide logarithmic runtimes w.h.p. on all their operations. SKEAP and SEAP provide logarithmic runtimes w.h.p. on all their operations with SEAP having to use only O(log n) bit messages.

## 2018

Breaking the $\tilde\Omega(\sqrt{n})$ Barrier: Fast Consensus under a Late Adversary

P. Robinson, C. Scheideler, A. Setzer, in: Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2018

We study the consensus problem in a synchronous distributed system of n nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires $\tilde \Omega(\sqrt n)$ rounds in an n-node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginning of the previous round and unlimited computational power, but is oblivious to the current state of the nodes. Our main contributions are randomized distributed algorithms that achieve consensus with high probability among all except a small constant fraction of the nodes (i.e., "almost-everywhere'') against a late adaptive adversary who can block up to ε n$nodes in each round, for a small constant ε >0$. Our first protocol achieves binary almost-everywhere consensus and also guarantees a decision on the majority input value, thus ensuring plurality consensus. We also present an algorithm that achieves the same time complexity for multi-value consensus. Both of our algorithms succeed in $O(log n)$ rounds with high probability, thus showing an exponential gap to the $\tilde\Omega(\sqrt n)$ lower bound of Ben-Or and Bar-Joseph for strongly adaptive crash-failure adversaries, which can be strengthened to $\Omega(n)$ when allowing the adversary to block nodes instead of permanently crashing them. Our algorithms are scalable to large systems as each node contacts only an (amortized) constant number of peers in each communication round. We show that our algorithms are optimal up to constant (resp.\ sub-logarithmic) factors by proving that every almost-everywhere consensus protocol takes $\Omega(log_d n)$ rounds in the worst case, where d is an upper bound on the number of communication requests initiated per node in each round. We complement our theoretical results with an experimental evaluation of the binary almost-everywhere consensus protocol revealing a short convergence time even against an adversary blocking a large fraction of nodes.

Forming Tile Shapes with Simple Robots

R. Gmyr, K. Hinnenthal, I. Kostitsyna, F. Kuhn, D. Rudolph, C. Scheideler, T.F. Strothmann, in: Proceedings of the 24th International Conference on DNA Computing and Molecular Programming, Springer International Publishing, 2018, pp. 122-138

Relays: Towards a Link Layer for Robust and Secure Fog Computing

C. Scheideler, in: Proceedings of the 2018 Workshop on Theory and Practice for Integrated Cloud, Fog and Edge Computing Paradigms, TOPIC@PODC 2018, Egham, United Kingdom, July 27, 2018, 2018, pp. 1-2

Self-stabilizing Overlays for high-dimensional Monotonic Searchability

M. Feldmann, C. Kolb, C. Scheideler, in: Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Springer, Cham, 2018, pp. 16-31

We extend the concept of monotonic searchability~\cite{DBLP:conf/opodis/ScheidelerSS15}~\cite{DBLP:conf/wdag/ScheidelerSS16} for self-stabilizing systems from one to multiple dimensions. A system is self-stabilizing if it can recover to a legitimate state from any initial illegal state. These kind of systems are most often used in distributed applications. Monotonic searchability provides guarantees when searching for nodes while the recovery process is going on. More precisely, if a search request started at some node $u$ succeeds in reaching its destination $v$, then all future search requests from $u$ to $v$ succeed as well. Although there already exists a self-stabilizing protocol for a two-dimensional topology~\cite{DBLP:journals/tcs/JacobRSS12} and an universal approach for monotonic searchability~\cite{DBLP:conf/wdag/ScheidelerSS16}, it is not clear how both of these concepts fit together effectively. The latter concept even comes with some restrictive assumptions on messages, which is not the case for our protocol. We propose a simple novel protocol for a self-stabilizing two-dimensional quadtree that satisfies monotonic searchability. Our protocol can easily be extended to higher dimensions and offers routing in $\mathcal O(\log n)$ hops for any search request.

A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension

M. Benter, T. Knollmann, F. Meyer auf der Heide, A. Setzer, J. Sundermeier, in: Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD), 2018

We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\ The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07). We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range. Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds. Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.

Brief Announcement: Competitive Routing in Hybrid Communication Networks

D. Jung, C. Kolb, C. Scheideler, J. Sundermeier, in: Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA), ACM Press, 2018

On Underlay-Aware Self-Stabilizing Overlay Networks

T. Götte, C. Scheideler, A. Setzer, in: Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018), Springer, 2018, pp. 50-64

We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of their shortest path in the tree. We rigorously prove that our protocol works correctly under asynchronous and non-FIFO message delivery. Further, the protocol stabilizes after O(N^2) asynchronous rounds where N is the number of nodes in the overlay.

Shape Recognition by a Finite Automaton Robot

R. Gmyr, K. Hinnenthal, I. Kostitsyna, F. Kuhn, D. Rudolph, C. Scheideler, in: 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK, 2018, pp. 52:1-52:15

Self-Stabilizing Supervised Publish-Subscribe Systems

M. Feldmann, C. Kolb, C. Scheideler, T.F. Strothmann, in: Proceedings of the 32nd IEEE International Parallel & Distributed Processing Symposium (IPDPS), IEEE, 2018

In this paper we present two major results: First, we introduce the first self-stabilizing version of a supervised overlay network (as introduced in~\cite{DBLP:conf/ispan/KothapalliS05}) by presenting a self-stabilizing supervised skip ring. Secondly, we show how to use the self-stabilizing supervised skip ring to construct an efficient self-stabilizing publish-subscribe system. That is, in addition to stabilizing the overlay network, every subscriber of a topic will eventually know all of the publications that have been issued so far for that topic. The communication work needed to processes a subscribe or unsubscribe operation is just a constant in a legitimate state, and the communication work of checking whether the system is still in a legitimate state is just a constant on expectation for the supervisor as well as any process in the system.

Relays: A New Approach for the Finite Departure Problem in Overlay Networks

C. Scheideler, A. Setzer, in: Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018), 2018

A fundamental problem for overlay networks is to safely exclude leaving nodes, i.e., the nodes requesting to leave the overlay network are excluded from it without affecting its connectivity. To rigorously study self-stabilizing solutions to this problem, the Finite Departure Problem (FDP) has been proposed [9]. In the FDP we are given a network of processes in an arbitrary state, and the goal is to eventually arrive at (and stay in) a state in which all leaving processes irrevocably decided to leave the system while for all weakly-connected components in the initial overlay network, all staying processes in that component will still form a weakly connected component. In the standard interconnection model, the FDP is known to be unsolvable by local control protocols, so oracles have been investigated that allow the problem to be solved [9]. To avoid the use of oracles, we introduce a new interconnection model based on relays. Despite the relay model appearing to be rather restrictive, we show that it is universal, i.e., it is possible to transform any weakly-connected topology into any other weakly-connected topology, which is important for being a useful interconnection model for overlay networks. Apart from this, our model allows processes to grant and revoke access rights, which is why we believe it to be of interest beyond the scope of this paper. We show how to implement the relay layer in a self-stabilizing way and identify properties protocols need to satisfy so that the relay layer can recover while serving protocol requests.

Skueue: A Scalable and Sequentially Consistent Distributed Queue

M. Feldmann, C. Scheideler, A. Setzer, in: Proceedings of the 32nd IEEE International Parallel & Distributed Processing Symposium (IPDPS), IEEE, 2018

We propose a distributed protocol for a queue, called Skueue, which spreads its data fairly onto multiple processes, avoiding bottlenecks in high throughput scenarios. Skueuecan be used in highly dynamic environments, through the addition of join and leave requests to the standard queue operations enqueue and dequeue. Furthermore Skueue satisfies sequential consistency in the asynchronous message passing model. Scalability is achieved by aggregating multiple requests to a batch, which can then be processed in a distributed fashion without hurting the queue semantics. Operations in Skueue need a logarithmic number of rounds w.h.p. until they are processed, even under a high rate of incoming requests.

On the runtime of universal coating for programmable matter

J. J. Daymude, Z. Derakhshandeh, R. Gmyr, A. Porter, A. W. Richa, C. Scheideler, T.F. Strothmann, Natural Computing (2018)(1), pp. 81--96

A Self-Stabilizing Hashed Patricia Trie

T. Knollmann, C. Scheideler, in: Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Springer, Cham, 2018

While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, we present a self-stabilizing protocol for a distributed data structure called the hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has a wide area of applications including string matching problems while offering low overhead and efficient operations when embedded on top of a distributed hash table. Especially, longest prefix matching for $x$ can be done in $\mathcal{O}(\log |x|)$ hash table read accesses. We show how to maintain the structure in a self-stabilizing way. Our protocol assures low overhead in a legal state and a total (asymptotically optimal) memory demand of $\Theta(d)$ bits, where $d$ is the number of bits needed for storing all keys.

Provably Anonymous Communication Based on Trusted Execution Environments

J. Blömer, J. Bobolz, C. Scheideler, A. Setzer, 2018

In this paper, we investigate the use of trusted execution environments (TEEs, such as Intel's SGX) for an anonymous communication infrastructure over untrusted networks. For this, we present the general idea of exploiting trusted execution environments for the purpose of anonymous communication, including a continuous-time security framework that models strong anonymity guarantees in the presence of an adversary that observes all network traffic and can adaptively corrupt a constant fraction of participating nodes. In our framework, a participating node can generate a number of unlinkable pseudonyms. Messages are sent from and to pseudonyms, allowing both senders and receivers of messages to remain anonymous. We introduce a concrete construction, which shows viability of our TEE-based approach to anonymous communication. The construction draws from techniques from cryptography and overlay networks. Our techniques are very general and can be used as a basis for future constructions with similar goals.

Competitive Routing in Hybrid Communication Networks

D. Jung, C. Kolb, C. Scheideler, J. Sundermeier, in: Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS) , Springer, 2018

Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion. In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work.

Preface

C. Scheideler, Theor. Comput. Sci. (2018), 751, pp. 1

## 2017

Distributed Monitoring of Network Properties: The Power of Hybrid Networks

R. Gmyr, K. Hinnenthal, C. Scheideler, C. Sohler, in: Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP), 2017, pp. 137:1--137:15

We initiate the study of network monitoring algorithms in a class of hybrid networks in which the nodes are connected by an external network and an internal network (as a short form for externally and internally controlled network). While the external network lies outside of the control of the nodes (or in our case, the monitoring protocol running in them) and might be exposed to continuous changes, the internal network is fully under the control of the nodes. As an example, consider a group of users with mobile devices having access to the cell phone infrastructure. While the network formed by the WiFi connections of the devices is an external network (as its structure is not necessarily under the control of the monitoring protocol), the connections between the devices via the cell phone infrastructure represent an internal network (as it can be controlled by the monitoring protocol). Our goal is to continuously monitor properties of the external network with the help of the internal network. We present scalable distributed algorithms that efficiently monitor the number of edges, the average node degree, the clustering coefficient, the bipartiteness, and the weight of a minimum spanning tree. Their performance bounds demonstrate that monitoring the external network state with the help of an internal network can be done much more efficiently than just using the external network, as is usually done in the literature.

Algorithmic Foundations of Programmable Matter Dagstuhl Seminar 16271

S. P. Fekete, A. W. Richa, K. Römer, C. Scheideler, SIGACT News (2017)(2), pp. 87--94

Self-Stabilizing Spanners for Tree Metrics

T. Götte, Masterarbeit, Universität Paderborn, 2017

Self-* Algorithms for Distributed Systems

T.F. Strothmann, Universität Paderborn, 2017

A Self-Stabilizing General De Bruijn Graph

M. Feldmann, C. Scheideler, in: Proceedings of the 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Springer, Cham, 2017, pp. 250-264

Searching for other participants is one of the most important operations in a distributed system.We are interested in topologies in which it is possible to route a packet in a fixed number of hops until it arrives at its destination.Given a constant $d$, this paper introduces a new self-stabilizing protocol for the $q$-ary $d$-dimensional de Bruijn graph ($q = \sqrt[d]{n}$) that is able to route any search request in at most $d$ hops w.h.p., while significantly lowering the node degree compared to the clique: We require nodes to have a degree of $\mathcal O(\sqrt[d]{n})$, which is asymptotically optimal for a fixed diameter $d$.The protocol keeps the expected amount of edge redirections per node in $\mathcal O(\sqrt[d]{n})$, when the number of nodes in the system increases by factor $2^d$.The number of messages that are periodically sent out by nodes is constant.

Universal coating for programmable matter

Z. Derakhshandeh, R. Gmyr, A. W. Richa, C. Scheideler, T.F. Strothmann, Theor. Comput. Sci. (2017), pp. 56--68

Sade: competitive MAC under adversarial SINR

A. Ogierman, A. Richa, C. Scheideler, S. Schmid, J. Zhang, Distributed Computing (2017), 31(3), pp. 241-254

This paper considers the problem of how to efficiently share a wireless medium which is subject to harsh external interference or even jamming. So far, this problem is understood only in simplistic single-hop or unit disk graph models. We in this paper initiate the study of MAC protocols for the SINR interference model (a.k.a. physical model). This paper makes two contributions. First, we introduce a new adversarial SINR model which captures a wide range of interference phenomena. Concretely, we consider a powerful, adaptive adversary which can jam nodes at arbitrary times and which is only limited by some energy budget. Our second contribution is a distributed MAC protocol called Sade which provably achieves a constant competitive throughput in this environment: we show that, with high probability, the protocol ensures that a constant fraction of the non-blocked time periods is used for successful transmissions.

Improved Leader Election for Self-organizing Programmable Matter

J. J. Daymude, R. Gmyr, A. W. Richa, C. Scheideler, T.F. Strothmann, in: Algorithms for Sensor Systems - 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2017, Vienna, Austria, September 7-8, 2017, Revised Selected Papers, 2017, pp. 127--140

Towards a universal approach for the finite departure problem in overlay networks

A. Koutsopoulos, C. Scheideler, T.F. Strothmann, Inf. Comput. (2017), pp. 408--424

A Self-Stabilizing Protocol for Graphs of Diameter Two

T. Knollmann, Masterarbeit, Universität Paderborn, 2017

## 2016

Self-stabilizing Metric Graphs

R. Gmyr, J. Lefèvre, C. Scheideler, in: Proceedings of the 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), 2016, pp. 248--262

We present a self-stabilizing algorithm for overlay networks that, for an arbitrary metric given by a distance oracle, constructs the graph representing that metric. The graph representing a metric is the unique minimal undirected graph such that for any pair of nodes the length of a shortest path between the nodes corresponds to the distance between the nodes according to the metric. The algorithm works under both an asynchronous and a synchronous daemon. In the synchronous case, the algorithm stablizes in time O(n) and it is almost silent in that after stabilization a node sends and receives a constant number of messages per round.

Universal Shape Formation for Programmable Matter

Z. Derakhshandeh, R. Gmyr, A. W. Richa, C. Scheideler, T.F. Strothmann, in: Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016, Asilomar State Beach/Pacific Grove, CA, USA, July 11-13, 2016, ACM, 2016, pp. 289--299

Jamming-Resistant MAC Protocols for Wireless Networks

A. W. Richa, C. Scheideler, in: Encyclopedia of Algorithms, 2016, pp. 999--1002

Systematic evaluation of peer-to-peer systems using PeerfactSim.KOM

M. Feldotto, K. Graffi, Concurrency and Computation: Practice and Experience (2016), 28(5), pp. 1655-1677

Comparative evaluations of peer-to-peer protocols through simulations are a viable approach to judge the performance and costs of the individual protocols in large-scale networks. In order to support this work, we present the peer-to-peer system simulator PeerfactSim.KOM, which we extended over the last years. PeerfactSim.KOM comes with an extensive layer model to support various facets and protocols of peer-to-peer networking. In this article, we describe PeerfactSim.KOM and show how it can be used for detailed measurements of large-scale peer-to-peer networks. We enhanced PeerfactSim.KOM with a fine-grained analyzer concept, with exhaustive automated measurements and gnuplot generators as well as a coordination control to evaluate sets of experiment setups in parallel. Thus, by configuring all experiments and protocols only once and starting the simulator, all desired measurements are performed, analyzed, evaluated, and combined, resulting in a holistic environment for the comparative evaluation of peer-to-peer systems. An immediate comparison of different configurations and overlays under different aspects is possible directly after the execution without any manual post-processing.

Churn- and DoS-resistant Overlay Networks Based on Network Reconfiguration

M. Drees, R. Gmyr, C. Scheideler, in: Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2016, pp. 417--427

We present three robust overlay networks: First, we present a network that organizes the nodes into an expander and is resistant to even massive adversarial churn. Second, we develop a network based on the hypercube that maintains connectivity under adversarial DoS-attacks. For the DoS-attacks we use the notion of a Omega(log log n)-late adversary which only has access to topological information that is at least Omega(log log n) rounds old. Finally, we develop a network that combines both churn- and DoS-resistance. The networks gain their robustness through constant network reconfiguration, i.e., the topology of the networks changes constantly. Our reconguration algorithms are based on node sampling primitives for expanders and hypercubes that allow each node to sample a logarithmic number of nodes uniformly at random in O(log log n) communication rounds. These primitives are specific to overlay networks and their optimal runtime represents an exponential improvement over known techniques. Our results have a wide range of applications, for example in the area of scalable and robust peer-to-peer systems.

Aggregation in Overlay Networks

K. Hinnenthal, Masterarbeit, Universität Paderborn, 2016

We consider the problem of aggregation in overlay networks. We use a synchronous time model in which each node has polylogarithmic memory and can send at most a polylogarithmic number of messages per round. We investigate how to quickly compute the result of an aggregate functionf over elements that are distributed among the nodes of the network such that the result is eventually known by a selected root node. We show how to compute distributive aggregate functions such as SUM, MAX, and OR in time $O(\log n / \log\log n)$ using a tree that is created in a pre-processing phase. If only a polylogarithmic number of data items need to be aggregated, we show how to compute the result in time $O(\sqrt{\log n / \log\log n})$. Furthermore, we show how to compute holistic aggregate functions such as DISTINCT, SMALLEST(k) and MODE(k) in time $O(\log n / \log\log n)$. Finally, we show a lower bound of $\Omega(\sqrt{\log n / \log\log n})$ for deterministic algorithms that compute any of the aggregate functions in the scope of the thesis.

SplayNet: Towards Locally Self-Adjusting Networks

S. Schmid, C. Avin, C. Scheideler, M. Borokhovich, B. Haeupler, Z. Lotker, IEEE/ACM Trans. Netw. (2016)(3), pp. 1421--1433

The Impact of Communication Patterns on Distributed Self-Adjusting Binary Search Tree

T.F. Strothmann, Journal of Graph Algorithms and Applications (2016), 20(1), pp. 79-100

This paper introduces the problem of communication pattern adaption for a distributed self-adjusting binary search tree. We propose a simple local algorithm that is closely related to the over thirty-year-old idea of splay trees and evaluate its adaption performance in the distributed scenario if different communication patterns are provided. To do so, the process of self-adjustment is modeled similarly to a basic network creation game in which the nodes want to communicate with only a certain subset of all nodes. We show that, in general, the game (i.e., the process of local adjustments) does not converge, and that convergence is related to certain structures of the communication interests, which we call conflicts. We classify conflicts and show that for two communication scenarios in which convergence is guaranteed, the self-adjusting tree performs well. Furthermore, we investigate the different classes of conflicts separately and show that, for a certain class of conflicts, the performance of the tree network is asymptotically as good as the performance for converging instances. However, for the other conflict classes, a distributed self-adjusting binary search tree adapts poorly.

Towards a Universal Approach for Monotonic Searchability in Self-stabilizing Overlay Networks

C. Scheideler, A. Setzer, T.F. Strothmann, in: Proceedings of the 30th International Symposium on Distributed Computing (DISC), 2016, pp. 71--84

For overlay networks, the ability to recover from a variety of problems like membership changes or faults is a key element to preserve their functionality. In recent years, various self-stabilizing overlay networks have been proposed that have the advantage of being able to recover from any illegal state. However, the vast majority of these networks cannot give any guarantees on its functionality while the recovery process is going on. We are especially interested in searchability, i.e., the functionality that search messages for a specific identifier are answered successfully if a node with that identifier exists in the network. We investigate overlay networks that are not only self-stabilizing but that also ensure that monotonic searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. Monotonic searchability was recently introduced in OPODIS 2015, in which the authors provide a solution for a simple line topology.We present the first universal approach to maintain monotonic searchability that is applicable to a wide range of topologies. As the base for our approach, we introduce a set of primitives for manipulating overlay networks that allows us to maintain searchability and show how existing protocols can be transformed to use theses primitives.We complement this result with a generic search protocol that together with the use of our primitives guarantees monotonic searchability.As an additional feature, searching existing nodes with the generic search protocol is as fast as searching a node with any other fixed routing protocol once the topology has stabilized.

On the Runtime of Universal Coating for Programmable Matter

Z. Derakhshandeh, R. Gmyr, A. Porter, A. W. Richa, C. Scheideler, T.F. Strothmann, in: DNA Computing and Molecular Programming - 22nd International Conference, DNA 22, Munich, Germany, September 4-8, 2016, Proceedings, 2016, pp. 148--164

## 2015

An Algorithmic Framework for Shape Formation Problems in Self-Organizing Particle Systems

Z. Derakhshandeh, R. Gmyr, A. W. Richa, C. Scheideler, T.F. Strothmann, in: Proceedings of the Second Annual International Conference on Nanoscale Computing and Communication, NANOCOM' 15, Boston, MA, USA, September 21-22, 2015, ACM, 2015, pp. 21:1--21:2

Brief Announcement: On the Feasibility of Leader Election and Shape Formation with Self-Organizing Programmable Matter

Z. Derakhshandeh, R. Gmyr, T.F. Strothmann, R. A. Bazzi, A. W. Richa, C. Scheideler, in: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebasti{\'{a}}n, Spain, July 21 - 23, 2015, ACM, 2015, pp. 67--69

A deterministic worst-case message complexity optimal solution for resource discovery

S. Kniesburges, A. Koutsopoulos, C. Scheideler, Theoretical Computer Science (2015), pp. 67-79

We consider the problem of resource discovery in distributed systems. In particular we give an algorithm, such that each node in a network discovers the address of any other node in the network. We model the knowledge of the nodes as a virtual overlay network given by a directed graph such that complete knowledge of all nodes corresponds to a complete graph in the overlay network. Although there are several solutions for resource discovery, our solution is the first that achieves worst-case optimal work for each node, i.e. the number of addresses (O(n)O(n)) or bits (O(nlog⁡n)O(nlog⁡n)) a node receives or sends coincides with the lower bound, while ensuring only a linear runtime (O(n)O(n)) on the number of rounds.

Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures

C. Scheideler, A. Setzer, T.F. Strothmann, in: Proceedings of the 19th International Conference on Principles of Distributed Systems (OPODIS), 2015

Distributed applications are commonly based on overlay networks interconnecting their sites so that they can exchange information. For these overlay networks to preserve their functionality, they should be able to recover from various problems like membership changes or faults. Various self-stabilizing overlay networks have already been proposed in recent years, which have the advantage of being able to recover from any illegal state, but none of these networks can give any guarantees on its functionality while the recovery process is going on. We initiate research on overlay networks that are not only self-stabilizing but that also ensure that searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. We call this property monotonic searchability. We show that in general it is impossible to provide monotonic searchability if corrupted messages are present in the system, which justifies the restriction to system states without corrupted messages. Furthermore, we provide a self-stabilizing protocol for the line for which we can also show monotonic searchability. It turns out that even for the line it is non-trivial to achieve this property. Additionally, we extend our protocol to deal with node departures in terms of the Finite Departure Problem of Foreback et. al (SSS 2014). This makes our protocol even capable of handling node dynamics.

Brief Announcement: Towards a Universal Approach for the Finite Departure Problem in Overlay Networks

A. Koutsopoulos, C. Scheideler, T.F. Strothmann, in: Proceedings of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2015, Portland, OR, USA, June 13-15, 2015, ACM, 2015, pp. 77--79

IRIS: A Robust Information System Against Insider DoS Attacks

M. Eikel, C. Scheideler, Transactions on Parallel Computing (2015)(3), pp. 18:1--18:33

In this work, we present the first scalable distributed information system, that is, a system with low storage overhead, that is provably robust against denial-of-service (DoS) attacks by a current insider. We allow a current insider to have complete knowledge about the information system and to have the power to block any ϵ-fraction of its servers by a DoS attack, where ϵ can be chosen up to a constant. The task of the system is to serve any collection of lookup requests with at most one per nonblocked server in an efficient way despite this attack. Previously, scalable solutions were only known for DoS attacks of past insiders, where a past insider only has complete knowledge about some past time point t0 of the information system. Scheideler et al. [Awerbuch and Scheideler 2007; Baumgart et al. 2009] showed that in this case, it is possible to design an information system so that any information that was inserted or last updated after t0 is safe against a DoS attack. But their constructions would not work at all for a current insider. The key idea behind our IRIS system is to make extensive use of coding. More precisely, we present two alternative distributed coding strategies with an at most logarithmic storage overhead that can handle up to a constant fraction of blocked servers.

Dynamics and Efficiency in Topological Self-Stabilization

A. Koutsopoulos, Universität Paderborn, 2015

Towards a Universal Approach for the Finite Departure Problem in Overlay Networks

A. Koutsopoulos, C. Scheideler, T.F. Strothmann, in: Proceedings of the 17th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), 2015, pp. 201-216

A fundamental problem for overlay networks is to safely exclude leaving nodes, i.e., the nodes requesting to leave the overlay network are excluded from it without affecting its connectivity. There are a number of studies for safe node exclusion if the overlay is in a well-defined state, but almost no formal results are known for the case in which the overlay network is in an arbitrary initial state, i.e., when looking for a self-stabilizing solution for excluding leaving nodes. We study this problem in two variants: the Finite Departure Problem (FDP) and the Finite Sleep Problem (FSP). In the FDP the leaving nodes have to irrevocably decide when it is safe to leave the network, whereas in the FSP, this leaving decision does not have to be final: the nodes may resume computation when woken up by an incoming message. We are the first to present a self-stabilizing protocol for the FDP and the FSP that can be combined with a large class of overlay maintenance protocols so that these are then guaranteed to safely exclude leaving nodes from the system from any initial state while operating as specified for the staying nodes. In order to formally define the properties these overlay maintenance protocols have to satisfy, we identify four basic primitives for manipulating edges in an overlay network that might be of independent interest.

Monotonic Searchability for distributed sorted Lists and De Bruijn Graphs

M. Feldmann, Masterarbeit, Universität Paderborn, 2015

Leader Election and Shape Formation with Self-organizing Programmable Matter

Z. Derakhshandeh, R. Gmyr, T.F. Strothmann, R. A. Bazzi, A. W. Richa, C. Scheideler, in: DNA Computing and Molecular Programming - 21st International Conference, DNA 21, Boston and Cambridge, MA, USA, August 17-21, 2015. Proceedings, 2015, pp. 117--132

The impact of communication patterns on distributed locally self-adjusting binary search trees

T.F. Strothmann, in: Proceedings of the 9th International Workshop on Algorithms and Computation (WALCOM), 2015, pp. 175--186

This paper introduces the problem of communication pattern adaption for a distributed self-adjusting binary search tree. We propose a simple local algorithm, which is closely related to the nearly thirty-year-old idea of splay trees and evaluate its adaption performance in the distributed scenario if different communication patterns are provided.To do so, the process of self-adjustment is modeled similarly to a basic network creation game, in which the nodes want to communicate with only a certain subset of all nodes. We show that, in general, the game (i.e., the process of local adjustments) does not converge, and convergence is related to certain structures of the communication interests, which we call conflicts.We classify conflicts and show that for two communication scenarios in which convergence is guaranteed, the self-adjusting tree performs well.Furthermore, we investigate the different classes of conflicts separately and show that, for a certain class of conflicts, the performance of the tree network is asymptotically as good as the performance for converging instances. However, for the other conflict classes, a distributed self-adjusting binary search tree adapts poorly.

## 2014

Brief announcement: amoebot - a new model for programmable matter

Z. Derakhshandeh, S. Dolev, R. Gmyr, A. W. Richa, C. Scheideler, T.F. Strothmann, in: 26th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'14, Prague, Czech Republic - June 23 - 25, 2014, ACM, 2014, pp. 220--222

RoBuSt: A Crash-Failure-Resistant Distributed Storage System

C. Scheideler, A. Setzer, M. Eikel, in: Proceedings of the 18th International Conference on Principles of Distributed Systems (OPODIS), 2014, pp. 107--122

In this work we present the first distributed storage system that is provably robust against crash failures issued by an adaptive adversary, i.e., for each batch of requests the adversary can decide based on the entire system state which servers will be unavailable for that batch of requests. Despite up to \gamma n^{1/\log\log n} crashed servers, with \gamma>0 constant and n denoting the number of servers, our system can correctly process any batch of lookup and write requests (with at most a polylogarithmic number of requests issued at each non-crashed server) in at most a polylogarithmic number of communication rounds, with at most polylogarithmic time and work at each server and only a logarithmic storage overhead. Our system is based on previous work by Eikel and Scheideler (SPAA 2013), who presented IRIS, a distributed information system that is provably robust against the same kind of crash failures. However, IRIS is only able to serve lookup requests. Handling both lookup and write requests has turned out to require major changes in the design of IRIS.

Competitive MAC under adversarial SINR

A. Ogierman, A.W. Richa, C. Scheideler, S. Schmid, J. Zhang, in: Proceedings of the 33rd Annual IEEE International Conference on Computer Communications (INFOCOM), 2014, pp. 2751--2759

This paper considers the problem of how to efficiently share a wireless medium which is subject to harsh external interference or even jamming. While this problem has already been studied intensively for simplistic single-hop or unit disk graph models, we make a leap forward and study MAC protocols for the SINR interference model (a.k.a. the physical model). We make two contributions. First, we introduce a new adversarial SINR model which captures a wide range of interference phenomena. Concretely, we consider a powerful, adaptive adversary which can jam nodes at arbitrary times and which is only limited by some energy budget. The second contribution of this paper is a distributed MAC protocol which provably achieves a constant competitive throughput in this environment: we show that, with high probability, the protocol ensures that a constant fraction of the non-blocked time periods is used for successful transmissions.

Algorithmic Aspects of Resource Management in the Cloud

S. Kniesburges, C. Markarian, F. Meyer auf der Heide, C. Scheideler, in: Proceedings of the 21st International Colloquium on Structural Information and Communication Complexity (SIROCCO), 2014, pp. 1-13

In this survey article, we discuss two algorithmic research areas that emerge from problems that arise when resources are offered in the cloud. The first area, online leasing, captures problems arising from the fact that resources in the cloud are not bought, but leased by cloud vendors. The second area, Distributed Storage Systems, deals with problems arising from so-called cloud federations, i.e., when several cloud providers are needed to fulfill a given task.

SKIP*: A Self-Stabilizing Skip Graph

R. Jacob, A. W. Richa, C. Scheideler, S. Schmid, H. Täubig, J. ACM (2014)(6), pp. 36:1--36:26

HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths

M. Feldotto, C. Scheideler, K. Graffi, in: Proceedings of the 14th IEEE International Conference on Peer-to-Peer Computing (P2P), 2014, pp. 1-10

In this paper we present and analyze HSkip+, a self-stabilizing overlay network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its self-stabilization mechanism significantly outperforms the self-stabilization mechanism proposed for Skip+. Also, the nodes are now ordered according to their bandwidths and not according to their identifiers. Various other solutions have already been proposed for overlay networks with heterogeneous bandwidths, but they are not self-stabilizing. In addition to HSkip+ being self-stabilizing, its performance is on par with the best previous bounds on the time and work for joining or leaving a network of peers of logarithmic diameter and degree and arbitrary bandwidths. Also, the dilation and congestion for routing messages is on par with the best previous bounds for such networks, so that HSkip+ combines the advantages of both worlds. Our theoretical investigations are backed by simulations demonstrating that HSkip+ is indeed performing much better than Skip+ and working correctly under high churn rates.

Minimum Linear Arrangement of Series-Parallel Graphs

C. Scheideler, M. Eikel, A. Setzer, in: Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA), 2014, pp. 168--180

We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time $O(|E|)$ and is very easy to implement. Its divide-and-conquer approach allows for an effective parallelization. Note that a suitable decomposition can also be computed in time $O(|E|\log{|E|})$ (or even $O(\log{|E|}\log^*{|E|})$ on an EREW PRAM using $O(|E|)$ processors). For the proof of the approximation ratio, we use a sophisticated charging method that uses techniques similar to amortized analysis in advanced data structures. On general graphs, the minimum linear arrangement problem is known to be NP-hard. To the best of our knowledge, the minimum linear arrangement problem on series-parallel graphs has not been studied before.

Re-Chord: A Self-stabilizing Chord Overlay Network

S. Kniesburges, A. Koutsopoulos, C. Scheideler, Theory of Computing Systems (2014)(3), pp. 591-612

The Chord peer-to-peer system is considered, together with CAN, Tapestry and Pastry, as one of the pioneering works on peer-to-peer distributed hash tables (DHT) that inspired a large volume of papers and projects on DHTs as well as peer-to-peer systems in general. Chord, in particular, has been studied thoroughly, and many variants of Chord have been presented that optimize various criteria. Also, several implementations of Chord are available on various platforms. Though Chord is known to be very efficient and scalable and it can handle churn quite well, no protocol is known yet that guarantees that Chord is self-stabilizing, i.e., the Chord network can be recovered from any initial state in which the network is still weakly connected. This is not too surprising since it is known that the Chord network is not locally checkable for its current topology. We present a slight extension of the Chord network, called Re-Chord (reactive Chord), that turns out to be locally checkable, and we present a self-stabilizing distributed protocol for it that can recover the Re-Chord network from any initial state, in which the n peers are weakly connected, in O(nlogn) communication rounds. We also show that our protocol allows a new peer to join or an old peer to leave an already stable Re-Chord network so that within O(logn)^2) communication rounds the Re-Chord network is stable again.

On Stabilizing Departures in Overlay Networks

D. Foreback, A. Koutsopoulos, M. Nesterenko, C. Scheideler, T.F. Strothmann, in: Proceedings of the 16th International Symposium on Stabilization, Safety, and Security of Distributed Systems, 2014, pp. 48--62

A fundamental problem for peer-to-peer systems is to maintain connectivity while nodes are leaving, i.e., the nodes requesting to leave the peer-to-peer system are excluded from the overlay network without affecting its connectivity. There are a number of studies for safe node exclusion if the overlay is in a well-defined state initially. Surprisingly, the problem is not formally studied yet for the case in which the overlay network is in an arbitrary initial state, i.e., when looking for a self-stabilizing solution for excluding leaving nodes. We study this problem in two variants: the Finite Departure Problem (FDP) ) and the Finite Sleep Problem (FSP). In the FDP the leaving nodes have to irrevocably decide when it is safe to leave the network, whereas in the FSP, this leaving decision does not have to be final: the nodes may resume computation if necessary. We show that there is no self-stabilizing distributed algorithm for the FDP, even in a synchronous message passing model. To allow a solution, we introduce an oracle called NIDEC and show that it is sufficient even for the asynchronous message passing model by proposing an algorithm that can solve the FDP using NIDEC. We also show that a solution to the FSP does not require an oracle.

Secure Distributed Data Structures for Peer-to-Peer-based Social Networks

J. Janiuk, A. Mäcker, K. Graffi, in: Proceedings of the International Conference on Collaboration Technologies and Systems (CTS), 2014, pp. 396-405

Online social networks are attracting billions of nowadays, both on a global scale as well as in social enterprise networks. Using distributed hash tables and peer-to-peer technology allows online social networks to be operated securely and efficiently only by using the resources of the user devices, thus alleviating censorship or data misuse by a single network operator. In this paper, we address the challenges that arise in implementing reliably and conveniently to use distributed data structures, such as lists or sets, in such a distributed hash-tablebased online social network. We present a secure, distributed list data structure that manages the list entries in several buckets in the distributed hash table. The list entries are authenticated, integrity is maintained and access control for single users and also groups is integrated. The approach for secure distributed lists is also applied for prefix trees and sets, and implemented and evaluated in a peer-to-peer framework for social networks. Evaluation shows that the distributed data structure is convenient and efficient to use and that the requirements on security hold.

Principles of Robust Medium Access and an Application to Leader Election

B. Awerbuch, A.W. Richa, C. Scheideler, S. Schmid, J. Zhang, Transactions on Algorithms (2014)(4)

This article studies the design of medium access control (MAC) protocols for wireless networks that are provably robust against arbitrary and unpredictable disruptions (e.g., due to unintentional external interference from co-existing networks or due to jamming). We consider a wireless network consisting of a set of n honest and reliable nodes within transmission (and interference) range of each other, and we model the external disruptions with a powerful adaptive adversary. This adversary may know the protocol and its entire history and can use this knowledge to jam the wireless channel at will at any time. It is allowed to jam a (1 − )-fraction of the timesteps, for an arbitrary constant > 0 unknown to the nodes. The nodes cannot distinguish between the adversarial jamming or a collision of two or more messages that are sent at the same time. We demonstrate, for the first time, that there is a local-control MAC protocol requiring only very limited knowledge about the adversary and the network that achieves a constant (asymptotically optimal) throughput for the nonjammed time periods under any of the aforementioned adversarial strategies. The derived principles are also useful to build robust applications on top of the MAC layer, and we present an exemplary study for leader election, one of the most fundamental tasks in distributed computing.

A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization

D. Gall, R. Jacob, A.W. Richa, C. Scheideler, S. Schmid, H.. Täubig, Theory of Computing Systems (2014)(1), pp. 110-135

Topological self-stabilization is an important concept to build robust open distributed systems (such as peer-to-peer systems) where nodes can organize themselves into meaningful network topologies. The goal is to devise distributed algorithms where nodes forward, insert, and delete links to neighboring nodes, and that converge quickly to such a desirable topology, independently of the initial network configuration. This article proposes a new model to study the parallel convergence time. Our model sheds light on the achievable parallelism by avoiding bottlenecks of existing models that can yield a distorted picture. As a case study, we consider local graph linearization—i.e., how to build a sorted list of the nodes of a connected graph in a distributed and self-stabilizing manner. In order to study the main structure and properties of our model, we propose two variants of a most simple local linearization algorithm. For each of these variants, we present analyses of the worst-case and bestcase parallel time complexities, as well as the performance under a greedy selection of the actions to be executed. It turns out that the analysis is non-trivial despite the simple setting, and to complement our formal insights we report on our experiments which indicate that the runtimes may be better in the average case.

## 2013

Competitive throughput in multi-hop wireless networks despite adaptive jamming

A. W. Richa, C. Scheideler, S. Schmid, J. Zhang, Distributed Computing (2013)(3), pp. 159--171

Corona: A stabilizing deterministic message-passing skip list

R. Mohd Nor, M. Nesterenko, C. Scheideler, Theor. Comput. Sci. (2013), pp. 119--129

CONE-DHT: A distributed self-stabilizing algorithm for a heterogeneous storage system

S. Kniesburges, A. Koutsopoulos, C. Scheideler, in: Proceedings of the 27th International Symposium on Distributed Computing (DISC), 2013, pp. 537-549

We consider the problem of managing a dynamic heterogeneous storagesystem in a distributed way so that the amount of data assigned to a hostin that system is related to its capacity. Two central problems have to be solvedfor this: (1) organizing the hosts in an overlay network with low degree and diameterso that one can efficiently check the correct distribution of the data androute between any two hosts, and (2) distributing the data among the hosts so thatthe distribution respects the capacities of the hosts and can easily be adapted asthe set of hosts or their capacities change. We present distributed protocols forthese problems that are self-stabilizing and that do not need any global knowledgeabout the system such as the number of nodes or the overall capacity of thesystem. Prior to this work no solution was known satisfying these properties.

Adding Capacity-Aware Storage Indirection to Homogeneous Distributed Hash Tables

P. Wette, K. Graffi, in: Proceedings of the Conference on Networked Systems (NetSys), 2013, pp. 35-42

Distributed hash tables are very versatile to use, as distributed storage is a desirable feature for various applications. Typical structured overlays like Chord, Pastry or Kademlia consider only homogeneous nodes with equal capacities, which does not resemble reality. In a practical use case, nodes might get overloaded by storing popular data. In this paper, we present a general approach to enable capacity awareness and load-balancing capability of homogeneous structured overlays. We introduce a hierarchical second structured overlay aside, which allows efficient capacity-based access on the nodes in the system as hosting mirrors. Simulation results show that the structured overlay is able to store various contents, such as of a social network, with only a negligible number of overloaded peers. Content, even if very popular, is hosted by easily findable capable peers. Thus, long-existing and well-evaluated overlays like Chord or Pastry can be used to create attractive DHT-based applications.

An Efficient and Fair MAC Protocol Robust to Reactive Interference

A. W. Richa, C. Scheideler, S. Schmid, J. Zhang, IEEE/ACM Trans. Netw. (2013)(3), pp. 760--771

Approximation Algorithms for the Linear Arrangement of Special Classes of Graphs

A. Setzer, Masterarbeit, Universität Paderborn, 2013

Bootstrapping Skynet: Calibration and Autonomic Self-Control of Structured Peer-to-Peer Networks

K. Graffi, T. Klerx, in: Proceedings of the International Conference on Peer-to-Peer Computing (P2P'13), 2013, pp. 1-5

Peer-to-peer systems scale to millions of nodes and provide routing and storage functions with best effort quality. In order to provide a guaranteed quality of the overlay functions, even under strong dynamics in the network with regard to peer capacities, online participation and usage patterns, we propose to calibrate the peer-to-peer overlay and to autonomously learn which qualities can be reached. For that, we simulate the peer-to-peer overlay systematically under a wide range of parameter configurations and use neural networks to learn the effects of the configurations on the quality metrics. Thus, by choosing a specific quality setting by the overlay operator, the network can tune itself to the learned parameter configurations that lead to the desired quality. Evaluation shows that the presented self-calibration succeeds in learning the configuration-quality interdependencies and that peer-to-peer systems can learn and adapt their behavior according to desired quality goals.

Locally Self-Adjusting Tree Networks

C. Avin, B. Häupler, Z. Lotker, C. Scheideler, S. Schmid, in: Proceedings of the 27th IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2013, pp. 395-406

This paper initiates the study of self-adjusting networks (or distributed data structures) whose topologies dynamically adapt to a communication pattern $\sigma$. We present a fully decentralized self-adjusting solution called SplayNet. A SplayNet is a distributed generalization of the classic splay tree concept. It ensures short paths (which can be found using local-greedy routing) between communication partners while minimizing topological rearrangements. We derive an upper bound for the amortized communication cost of a SplayNet based on empirical entropies of $\sigma$, and show that SplayNets have several interesting convergence properties. For instance, SplayNets features a provable online optimality under special requests scenarios. We also investigate the optimal static network and prove different lower bounds for the average communication cost based on graph cuts and on the empirical entropy of the communication pattern $\sigma$. From these lower bounds it follows, e.g., that SplayNets are optimal in scenarios where the requests follow a product distribution as well. Finally, this paper shows that in contrast to the Minimum Linear Arrangement problem which is generally NP-hard, the optimal static tree network can be computed in polynomial time for any guest graph, despite the exponentially large graph family. We complement our formal analysis with a small simulation study on a Facebook graph.

Symbiotic Coupling of P2P and Cloud Systems: The Wikipedia Case

K. Graffi, L. Bremer, in: Proceedings of the International Conference on Communications (ICC'13), 2013, pp. 3444 - 3449

Cloud computing offers high availability, dynamic scalability, and elasticity requiring only very little administration. However, this service comes with financial costs. Peer-to-peer systems, in contrast, operate at very low costs but cannot match the quality of service of the cloud. This paper focuses on the case study of Wikipedia and presents an approach to reduce the operational costs of hosting similar websites in the cloud by using a practical peer-to-peer approach. The visitors of the site are joining a Chord overlay, which acts as first cache for article lookups. Simulation results show, that up to 72% of the article lookups in Wikipedia could be answered by other visitors instead of using the cloud.

Comparative Evaluation of Peer-to-Peer Systems Using PeerfactSim.KOM

M. Feldotto, K. Graffi, in: Proceedings of the International Conference on High Performance Computing and Simulation (HPCS'13), 2013, pp. 99-106

Comparative evaluations of peer-to-peer protocols through simulations are a viable approach to judge the performance and costs of the individual protocols in large-scale networks. In order to support this work, we enhanced the peer-to-peer systems simulator PeerfactSim.KOM with a fine-grained analyzer concept, with exhaustive automated measurements and gnuplot generators as well as a coordination control to evaluate a set of experiment setups in parallel. Thus, by configuring all experiments and protocols only once and starting the simulator, all desired measurements are performed, analyzed, evaluated and combined, resulting in a holistic environment for the comparative evaluation of peer-to-peer systems.

IRIS: A Robust Information System Against Insider DoS-Attacks

M. Eikel, C. Scheideler, in: Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2013, pp. 119-129

In this work we present the first scalable distributed information system,i.e., a system with low storage overhead, that is provably robust againstDenial-of-Service (DoS) attacks by a current insider. We allow acurrent insider to have complete knowledge about the information systemand to have the power to block any \epsilon-fraction of its serversby a DoS-attack, where \epsilon can be chosen up to a constant. The taskof the system is to serve any collection of lookup requests with at most oneper non-blocked server in an efficient way despite this attack. Previously,scalable solutions were only known for DoS-attacks of past insiders, where apast insider only has complete knowledge about some past time pointt_0 of the information system. Scheideler et al. (DISC 2007, SPAA 2009) showedthat in this case it is possible to design an information system so that anyinformation that was inserted or last updated after t_0 is safe against a DoS-attack. But their constructions would not work at all for a current insider. The key idea behindour IRIS system is to make extensive use of coding. More precisely, we presenttwo alternative distributed coding strategies with an at most logarithmicstorage overhead that can handle up to a constant fraction of blocked servers.

A Deterministic Worst-Case Message Complexity Optimal Solution for Resource Discovery

S. Kniesburges, A. Koutsopoulos, C. Scheideler, in: Proceedings of 20th International Colloqium on Structural Information and Communication Complexity (SIROCCO), 2013, pp. 165-176

We consider the problem of resource discovery in distributed systems. In particular we give an algorithm, such that each node in a network discovers the add ress of any other node in the network. We model the knowledge of the nodes as a virtual overlay network given by a directed graph such that complete knowledge of all nodes corresponds to a complete graph in the overlay network. Although there are several solutions for resource discovery, our solution is the first that achieves worst-case optimal work for each node, i.e. the number of addresses (O(n)) or bits (O(nlogn)) a node receives or sendscoincides with the lower bound, while ensuring only a linearruntime (O(n)) on the number of rounds.

Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

P. Kolman, C. Scheideler, Theory of Computing Systems (2013)(2), pp. 341-363

An elementary h-route ow, for an integer h 1, is a set of h edge- disjoint paths between a source and a sink, each path carrying a unit of ow, and an h-route ow is a non-negative linear combination of elementary h-routeows. An h-route cut is a set of edges whose removal decreases the maximum h-route ow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and ows, for h 3: The size of a minimum h-route cut is at least f=h and at most O(log4 k f) where f is the size of the maximum h-routeow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log4 k). Previously, polylogarithmic approximation was known only for h-route cuts for h 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity ows and cuts. Similar results are shown also for the sparsest multiroute cut problem.

HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths

M. Feldotto, Masterarbeit, Universität Paderborn, 2013

Continuous Gossip-based Aggregation through Dynamic Information Aging

K. Graffi, V. Rapp, in: Proceedings of the International Conference on Computer Communications and Networks (ICCCN'13), 2013, pp. 1-7

Existing solutions for gossip-based aggregation in peer-to-peer networks use epochs to calculate a global estimation from an initial static set of local values. Once the estimation converges system-wide, a new epoch is started with fresh initial values. Long epochs result in precise estimations based on old measurements and short epochs result in imprecise aggregated estimations. In contrast to this approach, we present in this paper a continuous, epoch-less approach which considers fresh local values in every round of the gossip-based aggregation. By using an approach for dynamic information aging, inaccurate values and values from left peers fade from the aggregation memory. Evaluation shows that the presented approach for continuous information aggregation in peer-to-peer systems monitors the system performance precisely, adapts to changes and is lightweight to operate.

Ca-Re-Chord: A Churn Resistant Self-stabilizing Chord Overlay Network

K. Graffi, M. Benter, M. Divband, S. Kniesburges, A. Koutsopoulos, in: Proceedings of the Conference on Networked Systems (NetSys), 2013, pp. 27-34

Self-stabilization is the property of a system to transfer itself regardless of the initial state into a legitimate state. Chord as a simple, decentralized and scalable distributed hash table is an ideal showcase to introduce self-stabilization for p2p overlays. In this paper, we present Re-Chord, a self-stabilizing version of Chord. We show, that the stabilization process is functional, but prone to strong churn. For that, we present Ca-Re-Chord, a churn resistant version of Re-Chord, that allows the creation of a useful DHT in any kind of graph regardless of the initial state. Simulation results attest the churn resistance and good performance of Ca-Re-Chord.

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