max planck institut
informatik

# MPI-I-94-121

## Short random walks on graphs

### Barnes, Greg and Feige, Uriel

MPI-I-94-121. April 1994, 14 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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).
Acknowledgement:
References to related material:

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BibTeX
@TECHREPORT{BarnesFeige94,
AUTHOR = {Barnes, Greg and Feige, Uriel},
TITLE = {Short random walks on graphs},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
NUMBER = {MPI-I-94-121},
MONTH = {April},
YEAR = {1994},
ISSN = {0946-011X},
}