TY - JOUR
AB - 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.
AU - Gall, Dominik
AU - Jacob, Riko
AU - Richa, Andrea W.
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Täubig, Hanjo
ID - 464
IS - 1
JF - Theory of Computing Systems
TI - A Note on the Parallel Runtime of Self-Stabilizing Graph Linearization
ER -
TY - CONF
AB - 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.
AU - Foreback, Dianne
AU - Koutsopoulos, Andreas
AU - Nesterenko, Mikhail
AU - Scheideler, Christian
AU - Strothmann, Thim Frederik
ID - 393
T2 - Proceedings of the 16th International Symposium on Stabilization, Safety, and Security of Distributed Systems
TI - On Stabilizing Departures in Overlay Networks
ER -
TY - CONF
AB - 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.
AU - Scheideler, Christian
AU - Eikel, Martina
AU - Setzer, Alexander
ID - 397
T2 - Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)
TI - Minimum Linear Arrangement of Series-Parallel Graphs
ER -
TY - CONF
AB - 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.
AU - Feldotto, Matthias
AU - Scheideler, Christian
AU - Graffi, Kalman
ID - 412
T2 - Proceedings of the 14th IEEE International Conference on Peer-to-Peer Computing (P2P)
TI - HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths
ER -
TY - JOUR
AU - W. Richa, Andr{\'{e}}a
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 1868
IS - 3
JF - Distributed Computing
TI - Competitive throughput in multi-hop wireless networks despite adaptive jamming
ER -
TY - JOUR
AU - Mohd Nor, Rizal
AU - Nesterenko, Mikhail
AU - Scheideler, Christian
ID - 1870
JF - Theor. Comput. Sci.
TI - Corona: A stabilizing deterministic message-passing skip list
ER -
TY - JOUR
AU - W. Richa, Andrea
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 1871
IS - 3
JF - IEEE/ACM Trans. Netw.
TI - An Efficient and Fair MAC Protocol Robust to Reactive Interference
ER -
TY - JOUR
AB - 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.
AU - Kolman, Petr
AU - Scheideler, Christian
ID - 476
IS - 2
JF - Theory of Computing Systems
TI - Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
ER -
TY - CONF
AB - 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.
AU - Avin, Chen
AU - Häupler, Bernhard
AU - Lotker, Zvi
AU - Scheideler, Christian
AU - Schmid, Stefan
ID - 513
T2 - Proceedings of the 27th IEEE International Parallel and Distributed Processing Symposium (IPDPS)
TI - Locally Self-Adjusting Tree Networks
ER -
TY - CONF
AB - 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.
AU - Eikel, Martina
AU - Scheideler, Christian
ID - 519
T2 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - IRIS: A Robust Information System Against Insider DoS-Attacks
ER -