Compact Self-Stabilizing Leader Election for Arbitrary Networks

We present a self-stabilizing leader election algorithm for arbitrary networks, with spacecomplexity Opmaxtlog∆, log lognuq bits per node in n-node networks with maximum degree ∆. This space complexity is sub-logarithmic in n as long as ∆ “ n. The best space-complexity known so far for arbitrary networks was Oplog nq bits per node, and algorithms with sublogarithmic 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 Ωplognq bound for silent algorithms in arbitrary networks. Breaking this bound was obtained via the design of a (nonsilent) self-stabilizing algorithm using sophisticated tools such as solving the distance-2 coloring problem in a silent self-stabilizing manner, with space-complexity Opmaxtlog∆, log lognuq bits per node. Solving this latter coloring problem allows us to implement a sub-logarithmic encoding of spanning trees — storing the IDs of the neighbors requires Ωplognq bits per node, while we encode spanning trees using Opmaxtlog∆, log lognuq 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 Ωplog nq bits per node. Sorbonne Universités, UPMC Univ Paris 06, CNRS, Université d’Evry-Val-d’Essonne, LIP6 UMR 7606, 4 place Jussieu 75005, Paris. Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, 4 place Jussieu 75005, Paris.