Local Graph Partitioning using PageRank Vectors
Reid Andersen
Fan Chung
Kevin Lang
Dept. of Math., California Univ., La Jolla, CA;
This paper appears in: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Publication Date: Oct. 2006
On page(s): 475-486
Location: Berkeley, CA,
ISSN: 0272-5428
ISBN: 0-7695-2720-5
INSPEC Accession Number: 9297317
Digital Object Identifier: 10.1109/FOCS.2006.44
Current Version Published: 2006-12-19
Abstract
A local graph partitioning algorithm finds a cut near a specified starting vertex, with a running time that depends largely on the size of the small side of the cut, rather than the size of the input graph. In this paper, we present a local partitioning algorithm using a variation of PageRank with a specified starting distribution. We derive a mixing result for PageRank vectors similar to that for random walks, and show that the ordering of the vertices produced by a PageRank vector reveals a cut with small conductance. In particular, we show that for any set C with conductance Phi and volume k, a PageRank vector with a certain starting distribution can be used to produce a set with conductance (O(radic(Phi log k)). We present an improved algorithm for computing approximate PageRank vectors, which allows us to find such a set in time proportional to its size. In particular, we can find a cut with conductance at most oslash, whose small side has volume at least 2b in time O(2 log m/(2b log2 m/oslash2) where m is the number of edges in the graph. By combining small sets found by this local partitioning algorithm, we obtain a cut with conductance oslash and approximately optimal balance in time O(m log4 m/oslash)
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