Reid Andersen

STOC Conference 2009 Conference Paper

Finding sparse cuts locally using evolving sets

• Reid Andersen
• Yuval Peres

SODA Conference 2008 Conference Paper

A local algorithm for finding dense subgraphs

• Reid Andersen

SODA Conference 2008 Conference Paper

An algorithm for improving graph partitions

• Reid Andersen
• Kevin J. Lang

FOCS Conference 2006 Conference Paper

Local Graph Partitioning using PageRank Vectors

• Reid Andersen
• Fan R. K. Chung
• Kevin J. Lang

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 2 b in time O(2 log m/(2 b log 2 m/oslash 2 ) 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 log 4 m/oslash)