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Robustness of the rotor-router mechanism

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dc.contributor.author Bampas, E en
dc.contributor.author Gasieniec, L en
dc.contributor.author Klasing, R en
dc.contributor.author Kosowski, A en
dc.contributor.author Radzik, T en
dc.date.accessioned 2014-03-01T02:46:30Z
dc.date.available 2014-03-01T02:46:30Z
dc.date.issued 2009 en
dc.identifier.issn 03029743 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/32681
dc.subject Dynamic graphs en
dc.subject Graph exploration en
dc.subject Network faults en
dc.subject Propp machine en
dc.subject Rotor-router mechanism en
dc.subject.other De Bruijn en
dc.subject.other Dynamic changes en
dc.subject.other Dynamic graph en
dc.subject.other Ehrenfest en
dc.subject.other Eulerian cycles en
dc.subject.other Graph exploration en
dc.subject.other Graph G en
dc.subject.other Machine rotors en
dc.subject.other Router mechanisms en
dc.subject.other Single-agent en
dc.subject.other Spanning tree en
dc.subject.other Undirected graph en
dc.subject.other Routers en
dc.subject.other Graph theory en
dc.title Robustness of the rotor-router mechanism en
heal.type conferenceItem en
heal.identifier.primary 10.1007/978-3-642-10877-8_27 en
heal.identifier.secondary http://dx.doi.org/10.1007/978-3-642-10877-8_27 en
heal.publicationDate 2009 en
heal.abstract We consider the model of exploration of an undirected graph G by a single agent which is called the rotor-router mechanism or the Propp machine (among other names). Let πv indicate the edge adjacent to a node v which the agent took on its last exit from v. The next time when the agent enters node v, first a ""rotor"" at node v advances pointer πv to the edge which is next after the edge πv in a fixed cyclic order of the edges adjacent to v. Then the agent is directed onto edge πv to move to the next node. It was shown before that after initial O(mD) steps, the agent periodically follows one established Eulerian cycle, that is, in each period of 2m consecutive steps the agent traverses each edge exactly twice, once in each direction. The parameters m and D are the number of edges in G and the diameter of G. We investigate robustness of such exploration in presence of faults in the pointers πv or dynamic changes in the graph. We show that after the exploration establishes an Eulerian cycle, (i) if at some step the values of k pointers πv are arbitrarily changed, then a new Eulerian cycle is established within O(km) steps; (ii) if at some step k edges are added to the graph, then a new Eulerian cycle is established within O(km) steps; (iii) if at some step an edge is deleted from the graph, then a new Eulerian cycle is established within O(γm) steps, where γ is the smallest number of edges in a cycle in graph G containing the deleted edge. Our proofs are based on the relation between Eulerian cycles and spanning trees known as the ""BEST"" Theorem (after de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte). © 2009 Springer-Verlag. en
heal.journalName Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) en
dc.identifier.doi 10.1007/978-3-642-10877-8_27 en
dc.identifier.volume 5923 LNCS en
dc.identifier.spage 345 en
dc.identifier.epage 358 en


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