Article

How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)

Authors:

Michal Koucký,

Zvi LotkerAuthors Info & Claims

ICALP '08: Proceedings of the 35th international colloquium on Automata, Languages and Programming - Volume Part I

Pages 121 - 132

https://doi.org/10.1007/978-3-540-70575-8_11

Published: 07 July 2008 Publication History

Abstract

Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamicundirected 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 staticundirected 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 lazyrandom walk, that guarantees polynomial cover time regardless of the changes made by the adversary.

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How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image Guide Proceedings

ICALP '08: Proceedings of the 35th international colloquium on Automata, Languages and Programming - Volume Part I

July 2008

892 pages

ISBN:3540705740

Editors:
Luca Aceto
School of Computer Science, Reykjavik University, Reykjavík, Iceland 103
,
Ivan Damgård
Department of Computer Science, IT-Parken, University of Aarhus, ÅrhusN, Denmark 8200
,
Leslie Ann Goldberg
Department of Computer Science, University of Liverpool, Liverpool, UK L69 3BX
,
Magnús M. Halldórsson
School of Computer Science, Reykjavik University, Reykjavik, Iceland 103
,
Anna Ingólfsdóttir
Department of Computer Science, Reykjavik University, Reykjavík, Iceland 103
,
Igor Walukiewicz
Université de Bordeaux-1, LaBRI, Talence cedex, France 33405

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 July 2008

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Dinitz MFineman JGilbert SNewport C(2024)Smoothed Analysis of Information Spreading in Dynamic NetworksJournal of the ACM10.1145/366183171:3(1-24)Online publication date: 11-Jun-2024
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Kijima SShimizu NShiraga TMarx D(2021)How many vertices does a random walk miss in a network with moderately increasing the number of vertices?Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458072(106-122)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458072
Jahja IYu HHou R(2020)On the Power of Randomization in Distributed Algorithms in Dynamic Networks with Adaptive AdversariesEuro-Par 2020: Parallel Processing10.1007/978-3-030-57675-2_24(376-391)Online publication date: 24-Aug-2020
https://dl.acm.org/doi/10.1007/978-3-030-57675-2_24
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