Space Complexity of Self-stabilizing Leader Election in Passively-Mobile Anonymous Agents

Cai, Shukai; Izumi, Taisuke; Wada, Koichi

doi:10.1007/978-3-642-11476-2_10

Cited by 10 publications

(10 citation statements)

References 9 publications

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“…However, to solve the self-stabilizing leader election problem, n states are necessary and sufficient, where n is the number of agents. Thus the problem is unsolvable unless we generalize the population protocol model [8] (see also [25] for a similar result on mediated population protocol).…”

Section: Discussionmentioning

confidence: 99%

Probabilistic Self-Stabilization and Biased Random Walks on Dynamic Graphs

Yamashita

2012

IJNC

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A distributed system is said to be probabilistic self-stabilizing, if it eventually converges to a legitimate computation with probability 1, starting from any global configuration. Like a self-stabilizing system, a probabilistic self-stabilizing system tolerates any number of transient failures and recovers a legitimate computation, but only probabilistically, unlike a self-stabilizing system, which recovers it deterministically even in the worst case. However, a self-stabilizing algorithm is in general difficult to design and even impossible for some problems. A probabilistic self-stabilizing, on the other hand, is easier to design. To see this, we discuss how a probabilistic self-stabilizing system is constructible from a given weak stabilizing system, which can recover a legitimate computation only in the best case.An execution of a probabilistic self-stabilizing system can be modeled by a random walk on a graph, and its performance can be evaluated in terms of some quantities, e.g., the hitting and the cover times, of the corresponding random walk. The hitting and the cover times of random walks have been studied extensively, but most of them consider standard (i.e., unbiased) random walks on static graphs. We discuss how to design biased random walks whose hitting and cover times are faster than standard random walks, to improve the performance of probabilistic selfstabilizing system. We also discuss random walks on dynamic graphs to analyze a probabilistic self-stabilizing system such that its communication network topology frequently changes.

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Section: Discussionmentioning

confidence: 99%

Probabilistic Self-Stabilization and Biased Random Walks on Dynamic Graphs

Yamashita

2012

IJNC

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“…15 and Lem. 17) is tight for M ≥ n − |F| − 1 in the model with no mistakes, and for any protocol solving GP.…”

Section: Lower Bound For Gpmentioning

confidence: 95%

“…First, many other problems could be considered in the framework of population protocols enhanced by the notion of speed, e.g., round-robin token circulation, synchronization, coloring, consensus and leader election (cf. [3,9,15,18,31]). Second, in this first study of cover times, we have assumed that each pair of agents is repeatedly close enough to communicate.…”

Section: Future Workmentioning

confidence: 97%

On utilizing speed in networks of mobile agents

Beauquier

Burman

Clément

et al. 2010

Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

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International audiencePopulation protocols are a model presented recently for networks with a very large, possibly unknown number of mobile agents having small memory. This model has certain advantages over alternative models (such as DTN) for such networks. However, it was shown that the computational power of this model is limited to semi-linear predicates only. Hence, various extensions were suggested. We present a model that enhances the original model of population protocols by introducing a (weak) notion of speed of the agents. This enhancement allows us to design fast converging protocols with only weak requirements (for example, suppose that there are different types of agents, say agents attached to sick animals and to healthy animals, two meeting agents just need to be able to estimate which of them is faster, e.g., using their types, but not to actually know the speeds of their types). Then, using the new model, we study the gathering problem, in which there is an unknown number of anonymous agents that have values they should deliver to a base station (without replications). We develop efficient protocols step by step searching for an optimal solution and adapting to the size of the available memory. The protocols are simple, though their analysis is somewhat involved. We also present a more involved result - a lower bound on the length of the worst execution for any protocol. Our proofs introduce several techniques that may prove useful also in future studies of time in population protocols

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“…Self-stabilization [13] is an attractive concept to describe such self-repairing properties of an algorithm, and it has been intensively studied already, not only in terms of eventual stabilization but also in terms of guaranteed convergence times (see e.g., the works on time-adaptive self-stabilization such as [24]). Several self-stabilizing leader election protocols have been devised, e.g., [2,9,20] (see also the fault-contained solutions such as [15]). However, none of these approaches allows us to elect a leader in a wireless network that is exposed to harsh interference or even adaptive jamming.…”

Section: Related Workmentioning

confidence: 99%

Principles of Robust Medium Access and an Application to Leader Election

Awerbuch

Richa

Scheideler

et al. 2014

ACM Trans. Algorithms

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Abstract. 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 time steps, 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 non-jammed time periods under any adversarial strategy above. 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.1. Introduction. The efficient use of a shared medium is arguable one of the most relevant but also most complex problems in distributed computing. First, a wireless network requires distributed access coordination mechanisms which minimize the internal interference due to simultaneous transmissions from wireless devices in the same network. In addition, the availability of the wireless medium can vary significantly over time due to the external interference, e.g., due to disturbances from other sources such as microwaves, due to transmissions of co-existing (potentially mobile) networks, or due to intentional or even adversarial interruptions. Adversarial attacks constitute a major threat especially since they often do not require any special hardware and may be implemented by simply listening to the open medium and broadcasting in the same frequency band as the network.This article studies the design of distributed medium access schemes which are robust even against a powerful adversary who can block the medium at arbitrary and unpredictable times, and in an adaptive manner (i.e., depending on the protocol history). This adversarial model is used to capture a wide range of interference scenarios. Despite the adversary's power, we show that provably robust medium access solutions exist in the sense that in the time periods where the medium is available, there are many successful transmissions.

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Space Complexity of Self-stabilizing Leader Election in Passively-Mobile Anonymous Agents

Cited by 10 publications

References 9 publications

Probabilistic Self-Stabilization and Biased Random Walks on Dynamic Graphs

Probabilistic Self-Stabilization and Biased Random Walks on Dynamic Graphs

On utilizing speed in networks of mobile agents

Principles of Robust Medium Access and an Application to Leader Election

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