Local Graph Partitioning using PageRank Vectors | IEEE Conference Publication | IEEE Xplore

Local Graph Partitioning using PageRank Vectors


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, rath...Show More

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)
Date of Conference: 21-24 October 2006
Date Added to IEEE Xplore: 19 December 2006
Print ISBN:0-7695-2720-5
Print ISSN: 0272-5428
Conference Location: Berkeley, CA, USA
No metrics found for this document.

1 Introduction

One of the central problems in algorithmic design is the problem of finding a cut where the ratio between the number of edges crossing the cut and the size of the smaller side of the cut is small. There is a large literature of research papers on this topic, with applications in numerous areas.

No metrics found for this document.
Contact IEEE to Subscribe

References

References is not available for this document.