eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-02-28
24:1
24:12
10.4230/LIPIcs.OPODIS.2021.24
article
Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms
Blin, Lélia
1
https://orcid.org/0000-0003-0342-9243
Feuilloley, Laurent
2
https://orcid.org/0000-0002-3994-0898
Le Bouder, Gabriel
3
Sorbonne Université, Université d’Evry-Val-d’Essonne, CNRS, LIP6 UMR 7606, 4 place Jussieu, 75005 Paris, France
Univ. Lyon, Université Lyon 1, LIRIS UMR CNRS 5205, F-69621, Lyon, France
Sorbonne Université, CNRS, INRIA, LIP6 UMR 7606, 4 place Jussieu, 75005 Paris, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol217-opodis2021/LIPIcs.OPODIS.2021.24/LIPIcs.OPODIS.2021.24.pdf
Space lower bound
memory tight bound
self-stabilization
leader election
anonymous
identifiers
state model
ring topology