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Short random walks on graphs

Barnes, Greg and Feige, Uriel

April 1994, 14 pages.

Status: available - back from printing

We study the short term behavior of random walks on graphs, in particular, the rate at which a random walk discovers new vertices and edges. We prove a conjecture by Linial that the expected time to find $\cal N$ distinct vertices is $O({\cal N} ^ 3)$. We also prove an upper bound of $O({\cal M} ^ 2)$ on the expected time to traverse $\cal M$ edges, and $O(\cal M\cal N)$ on the expected time to either visit $\cal N$ vertices or traverse $\cal M$ edges (whichever comes first).

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  AUTHOR = {Barnes, Greg and Feige, Uriel},
  TITLE = {Short random walks on graphs},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-121},
  MONTH = {April},
  YEAR = {1994},
  ISSN = {0946-011X},