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Short random walks on graphs

MPS-Authors

Barnes,  Greg
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Feige,  Uriel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-94-121.pdf
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Citation

Barnes, G., & Feige, U.(1994). Short random walks on graphs (MPI-I-94-121). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B790-8
Abstract
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).