Polynomial deterministic rendezvous in arbitrary graphs

Dariusz R. Kowalski, Andrzej Pelc

Research output: Contribution to journalArticle

Abstract

The rendezvous problem in graphs has been extensively studied in the literature, mainly using a randomized approach. Two mobile agents have to meet at some node of a connected graph. We study deterministic algorithms for this problem, assuming that agents have distinct identifiers and are located in nodes of an unknown anonymous connected graph. Startup times of the agents are arbitrarily decided by the adversary. The measure of performance of a rendezvous algorithm is its cost: for a given initial location of agents in a graph, this is the number of steps since the startup of the later agent until rendezvous is achieved. Deterministic rendezvous has been previously shown feasible in arbitrary graphs [16] but the proposed algorithm had cost exponential in the number n of nodes and in the smaller identifier l, and polynomial in the difference τ between startup times. The following problem was stated in [16]: Does there exist a deterministic rendezvous algorithm with cost polynomial in n, τ and in labels L1, L2 of the agents (or even polynomial in n, τ and log L1, logL2)? We give a positive answer to both problems: our main result is a deterministic rendezvous algorithm with cost polynomial in n, τ and log l. We also show a lower bound Ω(n2) on the cost of rendezvous in some family of graphs.

Original languageEnglish (US)
Pages (from-to)644-656
Number of pages13
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3341
StatePublished - Dec 1 2004

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Rendezvous
Polynomials
Polynomial
Arbitrary
Graph in graph theory
Start-up
Costs
Connected graph
Mobile agents
Vertex of a graph
Labels
Mobile Agent
Deterministic Algorithm
Lower bound
Distinct
Unknown

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Polynomial deterministic rendezvous in arbitrary graphs. / Kowalski, Dariusz R.; Pelc, Andrzej.

In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 3341, 01.12.2004, p. 644-656.

Research output: Contribution to journalArticle

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