Uniform dynamic self-stabilizing leader election

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next crash is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic self-stabilizing protocols for leader election under read/write atomicity. Our protocols use randomization to break symmetry. We rst introduce self-stabilizing protocols for synchronization. Then, using the synchronization protocols we present a leader election protocol that stabilizes in O(D log n) time when the number of the processors is unknown and O(D), otherwise. We conclude this work by presenting a simple, uniform, self-stabilizing ranking protocol.

World Wide Web Conference Series, 1991

A distributed system is self-stabilizing if it can be started in any possible globalstate. Once started the system regains its consistency by itself, without any kindof outside intervention. The self-stabilization property makes the system tolerantto faults in which processors crash and then recover spontaneously in an arbitrarystate. When the intermediate period in between one recovery and the next crashis long

Parallel Processing Letters, 2008

We provide self-stabilizing algorithms to obtain and maintain a maximal matching, maximal independent set or minimal dominating set in a given system graph. They converge in linear rounds under a distributed or synchronous daemon. They can be implemented in an ad hoc network by piggy-backing on the beacon messages that nodes already use.

Lecture Notes in Computer Science, 2013

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the solution is required to be silent (i.e., when the state of each process remains fixed from some point in time during any execution), there exists a lower bound of Ω(log n) bits of memory per participating node , where n denotes the number of nodes in the system. This lower bound holds even in rings. We present a new deterministic (nonsilent) self-stabilizing protocol for n-node rings that uses only O(log log n) memory bits per node, and stabilizes in O(n log 2 n) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, it assumes an execution model that is used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) does not need to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides weak fairness, is assumed. Our result shows that, perhaps surprisingly, silence can be traded for an exponential decrease in memory space without significantly increasing stabilization time or introducing restrictive assumptions.

2003

In this paper we propose a new self-stabilizing distributed algorithm for minimal domination protocol in an arbitrary network graph using the synchronous model; the proposed protocol is general in the sense that it can stabilize with every possible minimal dominating set of the graph.

Lecture Notes in Computer Science, 2014

We propose a silent self-stabilizing leader election algorithm for bidirectional arbitrary connected identified networks. This algorithm is written in the locally shared memory model under the distributed unfair daemon. It requires no global knowledge on the network. Its stabilization time is in Θ(n 3) steps in the worst case, where n is the number of processes. Its memory requirement is asymptotically optimal, i.e., Θ(log n) bits per processes. Its round complexity is of the same order of magnitude-i.e., Θ(n) rounds-as the best existing algorithms designed with similar settings. To the best of our knowledge, this is the first self-stabilizing leader election algorithm for arbitrary identified networks that is proven to achieve a stabilization time polynomial in steps. By contrast, we show that the previous best existing algorithms designed with similar settings stabilize in a non polynomial number of steps in the worst case.

2017

We present the first self-stabilizing algorithm for leader election in arbitrary topologies whose space complexity is O(max{log Delta, log log n}) bits per node, where n is the network size and Delta its degree. This complexity is sub-logarithmic in n when Delta = n^o(1).

Lecture Notes in Computer Science, 1991

A self stabilizing protocol for constructing a rooted spanning tree in an arbitrary asynchronous network of processors that communicate through sha~ed memory is presented. The processors have unique identifiers but are otherwise identical. The network topology is assumed to be dynamic, that is, edges can join or leave the computation before it eventually stabilizes.

2020

This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT1 model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of Õ(n) messages, each of constant size, till stabilization, while stabilizing in Õ(n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n− 1) edges of T . In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms. The algorithm is relatively simpl...

Acta Informatica, 2007

We provide a novel model to formalize a well-known algorithm, by Chandra and Toueg, that solves Consensus among asynchronous distributed processes in the presence of a particular class of failure detectors (3S or, equivalently, Ω), under the hypothesis that only a minority of processes may crash. The model is defined as a global transition system that is unambigously generated by local transition rules. The model is syntax-free in that it does not refer to any form of programming language or pseudo code. We use our model to formally prove that the algorithm is correct. * The original publication is available at www.springerlink.com 1 Actually, the algorithm may easily reach system configurations in which, at a certain point in time, every process is coordinator in its current round, while all processes are in pairwise different rounds, by having every participant simply always suspect the respective coordinator. Analogously, the algorithm may easily reach moments in which none of the processes is the coordinator of its round. Moreover, in such a moment, it is impossible to predict, from a chronological point of view, which process will next become coordinator.