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More efficient periodic traversal in anonymous undirected graphs

hal.structure.identifierDépartement d'Informatique et d'Ingénierie [DII]
dc.contributor.authorCZYZOWICZ, Jurek
hal.structure.identifierInstitute of Mathematics
dc.contributor.authorDOBREV, Stefan
hal.structure.identifierDepartment of Computer Science [Liverpool]
dc.contributor.authorGĄSIENIEC, Leszek
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierAlgorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
dc.contributor.authorILCINKAS, David
hal.structure.identifierOchanomizu University
dc.contributor.authorJANSSON, Jesper
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierAlgorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
dc.contributor.authorKLASING, Ralf
hal.structure.identifierDepartment of Computer Science
dc.contributor.authorLIGNOS, Ioannis
hal.structure.identifierDepartment of Computer Science [Liverpool]
dc.contributor.authorMARTIN, Russell
hal.structure.identifierPrinciples of Informatics Research Division
dc.contributor.authorSADAKANE, Kunihiko
hal.structure.identifierDepartment of Computer Science
dc.contributor.authorSUNG, Wing-Kin
dc.date.accessioned2024-04-15T09:44:45Z
dc.date.available2024-04-15T09:44:45Z
dc.date.issued2012-07
dc.identifier.issn1879-2294
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/197870
dc.description.abstractEnWe consider the problem of periodic graph exploration in which a mobile entity with constant memory, an agent, has to visit all n nodes of an input simple, connected, undirected graph in a periodic manner. Graphs are assumed to be anonymous, that is, nodes are unlabeled. While visiting a node, the agent may distinguish between the edges incident to it; for each node v, the endpoints of the edges incident to v are uniquely identified by different integer labels called port numbers. We are interested in algorithms for assigning the port numbers together with traversal algorithms for agents using these port numbers to obtain short traversal periods. Periodic graph exploration is unsolvable if the port numbers are set arbitrarily; see Budach (1978) [1]. However, surprisingly small periods can be achieved by carefully assigning the port numbers. Dobrev et al. (2005) [4] described an algorithm for assigning port numbers and an oblivious agent (i.e., an agent with no memory) using it, such that the agent explores any graph with n nodes within the period 10n. When the agent has access to a constant number of memory bits, the optimal length of the period was proved in Gąsieniec et al. (2008) [7] to be no more than 3.75n−2 (using a different assignment of the port numbers and a different traversal algorithm). In this paper, we improve both these bounds. More precisely, we show how to achieve a period length of at most for oblivious agents and a period length of at most 3.5n−2 for agents with constant memory. To obtain our results, we introduce a new, fast graph decomposition technique called a three-layer partition that may also be useful for solving other graph problems in the future. Finally, we present the first non-trivial lower bound, 2.8n−2, on the period length for the oblivious case.
dc.description.sponsorshipAlgorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks
dc.language.isoen
dc.publisherElsevier
dc.subject.enAlgorithms and data structures
dc.subject.enGraph exploration
dc.subject.enPeriodic graph traversal
dc.subject.enOblivious agent
dc.subject.enConstant-memory agent
dc.subject.enThree-layer partition
dc.title.enMore efficient periodic traversal in anonymous undirected graphs
dc.typeArticle de revue
dc.identifier.doi10.1016/j.tcs.2012.01.035
dc.subject.halInformatique [cs]/Calcul parallèle, distribué et partagé [cs.DC]
dc.subject.halInformatique [cs]/Algorithme et structure de données [cs.DS]
bordeaux.journalTheoretical Computer Science
bordeaux.pagepages 60-76
bordeaux.volume444
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00726767
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00726767v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Theoretical%20Computer%20Science&rft.date=2012-07&rft.volume=444&rft.spage=pages%2060-76&rft.epage=pages%2060-76&rft.eissn=1879-2294&rft.issn=1879-2294&rft.au=CZYZOWICZ,%20Jurek&DOBREV,%20Stefan&G%C4%84SIENIEC,%20Leszek&ILCINKAS,%20David&JANSSON,%20Jesper&rft.genre=article


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