How to explore a fast-changing world (cover time of a simple random walk on evolving graphs)

Chen Avin, Michal Koucký, Zvi Lotker

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

138 Scopus citations

Abstract

Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamic undirected graphs with fixed underlying vertex set, i.e., graphs which are modified by inserting or deleting edges at every step of the walk. We are interested in the expected time needed to visit all the vertices of such a dynamic graph, the cover time, under the assumption that the graph is being modified by an oblivious adversary. It is well known that on connected static undirected graphs the cover time is polynomial in the size of the graph. On the contrary and somewhat counter-intuitively, we show that there are adversary strategies which force the expected cover time of a simple random walk on connected dynamic graphs to be exponential. We relate this result to the cover time of static directed graphs. In addition we provide a simple strategy, the lazy random walk, that guarantees polynomial cover time regardless of the changes made by the adversary.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
Pages121-132
Number of pages12
EditionPART 1
DOIs
StatePublished - 14 Aug 2008
Event35th International Colloquium on Automata, Languages and Programming, ICALP 2008 - Reykjavik, Iceland
Duration: 7 Jul 200811 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th International Colloquium on Automata, Languages and Programming, ICALP 2008
Country/TerritoryIceland
CityReykjavik
Period7/07/0811/07/08

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