An O(n log n) unidirectional distributed algorithm for extrema finding in a circle

Danny Dolev*, Maria Klawe, Michael Rodeh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

143 Scopus citations

Abstract

In this paper we present algorithms, which given a circular arrangement of n uniquely numbered processes, determine the maximum number in a distributive manner. We begin with a simple unidirectional algorithm, in which the number of messages passed is bounded by 2 n log n + O(n). By making several improvements to the simple algorithm, we obtain a unidirectional algorithm in which the number of messages passed is bounded by 1.5nlogn + O(n). These algorithms disprove Hirschberg and Sinclair's conjecture that O(n2) is a lower bound on the number of messages passed in undirectional algorithms for this problem. At the end of the paper we indicate how our methods can be used to improve an algorithm due to Peterson, to obtain a unidirectional algorithm using at most 1.356nlogn + O(n) messages. This is the best bound so far on the number of messages passed in both the bidirectional and unidirectional cases.

Original languageEnglish
Pages (from-to)245-260
Number of pages16
JournalJournal of Algorithms
Volume3
Issue number3
DOIs
StatePublished - Sep 1982
Externally publishedYes

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