2026-07-22T16:01:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15799 2024-03-06T10:56:11Z ddc:004 open_access

Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms Blin, Lélia Feuilloley, Laurent Le Bouder, Gabriel Space lower bound memory tight bound self-stabilization leader election anonymous identifiers state model ring topology Given a boolean predicate Π on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for Π is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying Π. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use Ω(log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Lélia Blin and Laurent Feuilloley and Gabriel Le Bouder 2022 Is Part Of LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.OPODIS.2021.24 urn:nbn:de:0030-drops-157997 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.24 eng https://creativecommons.org/licenses/by/4.0/legalcode