Robustness of the rotor-router mechanism

Bampas, E; Gasieniec, L; Klasing, R; Kosowski, A; Radzik, T

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