Euler tour lock-in problem in the rotor-router model: I choose pointers and you choose port numbers

Bampas, E; Gasieniec, L; Hanusse, N; Ilcinkas, D; Klasing, R; Kosowski, A

dc.contributor.author	Bampas, E	en
dc.contributor.author	Gasieniec, L	en
dc.contributor.author	Hanusse, N	en
dc.contributor.author	Ilcinkas, D	en
dc.contributor.author	Klasing, R	en
dc.contributor.author	Kosowski, A	en
dc.date.accessioned	2014-03-01T02:46:08Z
dc.date.available	2014-03-01T02:46:08Z
dc.date.issued	2009	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32570
dc.subject	Case Study	en
dc.subject	Random Walk	en
dc.subject.other	Euler tour	en
dc.subject.other	Initial configuration	en
dc.subject.other	Large diameter	en
dc.subject.other	Lock-in	en
dc.subject.other	Lock-in time	en
dc.subject.other	Non-trivial	en
dc.subject.other	Port numbers	en
dc.subject.other	Random Walk	en
dc.subject.other	Router mechanisms	en
dc.subject.other	Router model	en
dc.subject.other	Undirected graph	en
dc.title	Euler tour lock-in problem in the rotor-router model: I choose pointers and you choose port numbers	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-04355-0_44	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-04355-0_44	en
heal.publicationDate	2009	en
heal.abstract	The rotor-router model, also called the Propp machine, was first considered as a deterministic alternative to the random walk. It is known that the route in an undirected graph G=(V,E), where \|V\|=n and \|E\|=m, adopted by an agent controlled by the rotor-router mechanism forms eventually an Euler tour based on arcs obtained via replacing each edge in G by two arcs with opposite direction. The process of ushering the agent to an Euler tour is referred to as the lock-in problem. In recent work [11] Yanovski et al. proved that independently of the initial configuration of the rotor-router mechanism in G the agent locks-in in time bounded by 2mD, where D is the diameter of G. In this paper we examine the dependence of the lock-in time on the initial configuration of the rotor-router mechanism. The case study is performed in the form of a game between a player intending to lock-in the agent in an Euler tour as quickly as possible and its adversary with the counter objective. First, we observe that in certain (easy) cases the lock-in can be achieved in time O(m). On the other hand we show that if adversary is solely responsible for the assignment of ports and pointers, the lock-in time Ω(m•D) can be enforced in any graph with m edges and diameter D. Furthermore, we show that if provides its own port numbering after the initial setup of pointers by , the complexity of the lock-in problem is bounded by O(m • min {logm,D}). We also propose a class of graphs in which the lock-in requires time Ω(m •logm). In the remaining two cases we show that the lock-in requires time Ω(m •D) in graphs with the worst-case topology. In addition, however, we present non-trivial classes of graphs with a large diameter in which the lock-in time is O(m). © 2009 Springer Berlin Heidelberg.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-04355-0_44	en
dc.identifier.volume	5805 LNCS	en
dc.identifier.spage	423	en
dc.identifier.epage	435	en