On proof-labeling schemes versus silent self-stabilizing algorithms

Lélia Blin, Pierre Fraigniaud, Boaz Patt-Shamir

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

It follows from the definition of silent self-stabilization, and from the definition of proof-labeling scheme, that if there exists a silent self-stabilizing algorithm using l-bit registers for solving a task T, then there exists a proof-labeling scheme for T using registers of at most l bits. The first result in this paper is the converse to this statement. We show that if there exists a proof-labeling scheme for a task T, using l-bit registers, then there exists a silent self-stabilizing algorithm using registers of at most O(l + log n) bits for solving T, where n is the number of processes in the system. Therefore, as far as memory space is concerned, the design of silent self-stabilizing algorithms essentially boils down to the design of compact proof-labeling schemes. The second result in this paper addresses time complexity. We show that, for every task T with k-bits output size in n-node networks, there exists a silent self-stabilizing algorithm solving T in O(n) rounds, using registers of O(n2 + kn) bits. Therefore, as far as running time is concerned, every task has a silent self-stabilizing algorithm converging in a linear number of rounds.

Original languageEnglish
Title of host publicationStabilization, Safety and Security of Distributed Systems
EditorsPascal Felber, Vijay K. Garg
PublisherSpringer Verlag
Pages18-32
Number of pages15
ISBN (Electronic)9783319117638
DOIs
StatePublished - 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8756
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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