How to meet in anonymous network

Dariusz R. Kowalski, Adam Malinowski

Research output: Contribution to journalArticle

52 Scopus citations

Abstract

A set of k mobile agents with distinct identifiers and located in nodes of an unknown anonymous connected network, have to meet at some node. We show that this gathering problem is no harder than its special case for k = 2, called the rendezvous problem, and design deterministic protocols solving the rendezvous problem with arbitrary startups in rings and in general networks. The measure of performance is the number of steps since the startup of the last agent until the rendezvous is achieved. For rings we design an oblivious protocol with cost O (n log ℓ), where n is the size of the network and ℓ is the minimum label of participating agents. This result is asymptotically optimal due to the lower bound showed by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96]. For general networks we show a protocol with cost polynomial in n and log ℓ, independent of the maximum difference τ of startup times, which answers in the affirmative the open question by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96].

Original languageEnglish (US)
Pages (from-to)141-156
Number of pages16
JournalTheoretical Computer Science
Volume399
Issue number1-2
DOIs
StatePublished - Jun 3 2008
Externally publishedYes
Event13th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2006 - Chester, United Kingdom
Duration: Jul 2 2006Jul 5 2006

Keywords

  • Anonymous networks
  • Distributed algorithms
  • Gathering
  • Mobile agents
  • Rendezvous

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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