How many vertices does a random walk miss in a network with moderately increasing the number of vertices?

Shuji Kijima, Nobutaka Shimizu, Takeharu Shiraga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Real networks are often dynamic. In response to it, analyses of algorithms on dynamic networks attract more and more attention in network science and engineering. Random walks on dynamic graphs also have been investigated actively in more than a decade, where in most cases the edge set changes but the vertex set is static. The vertex sets are also dynamic in many real networks. Motivated by a new technology of the analysis of random walks on dynamic graphs, this paper introduces a simple model of graphs with an increasing number of vertices and presents an analysis of random walks associated with the cover time on such graphs. In particular, we reveal that a random walk asymptotically covers the vertices all but a constant number if the vertex set grows moderately.

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
PublisherAssociation for Computing Machinery
Pages106-122
Number of pages17
ISBN (Electronic)9781611976465
Publication statusPublished - 2021
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: Jan 10 2021Jan 13 2021

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/TerritoryUnited States
CityAlexandria, Virtual
Period1/10/211/13/21

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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