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Abstract
Introduction
Additional Related Work and Discussion
An Informal Overview
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Computer Science
Distributed Systems

Communication Efficient Self-Stabilizing Leader Election

Profile image of Shay KuttenShay Kutten

2020

https://doi.org/10.4230/LIPICS.DISC.2020.11
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Abstract

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...

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Communication Efficient Self-Stabilizing Leader Election (Full Version)
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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 $KT_{1}$ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of $\tilde{O} (n)$ messages, each of constant size, till stabilization, while stabilizing in $\tilde{O} (n)$ 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 algo...

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Brief Announcement: Compact Self-Stabilizing Leader Election in Arbitrary Graphs
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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).

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Lélia Blin

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We present a self-stabilizing leader election algorithm for general networks, with space-complexity O(log ∆+log log n) bits per node in n-node networks with maximum degree ∆. This space complexity is sub-logarithmic in n as long as ∆ = n o(1). The best space-complexity known so far for general networks was O(log n) bits per node, and algorithms with sub-logarithmic space-complexities were known for the ring only. To our knowledge, our algorithm is the first algorithm for self-stabilizing leader election to break the Ω(log n) bound for silent algorithms in general networks. Breaking this bound was obtained via the design of a (non-silent) self-stabilizing algorithm using sophisticated tools such as solving the distance-2 coloring problem in a silent self-stabilizing manner, with space-complexity O(log ∆ + log log n) bits per node. Solving this latter coloring problem allows us to implement a sublogarithmic encoding of spanning trees-storing the IDs of the neighbors requires Ω(log n) bits per node, while we encode spanning trees using O(log ∆+log log n) bits per node. Moreover, we show how to construct such compactly encoded spanning trees without relying on variables encoding distances or number of nodes, as these two types of variables would also require Ω(log n) bits per node.

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Lecture Notes in Computer Science, 2013

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Related topics

  • Computer Science
  • Self-stabilization
  • leader election
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