Fast approximate graph partitioning algorithms

Conference · Sun Jun 01 04:00:00 EDT 1997

OSTI ID:471721

Even, G ^[1]; Naor, J S ^[2]; Rao, S ^[3]; Schieber, B ^[4]

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1. Univ. des Saarlandes, Saarbruecken (Germany)
2. Technion, Haifa (Israel)
3. NEC Research Institute, Princeton, NJ (United States)
4. IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)

We study graph partitioning problems on graphs with edge capacities and vertex weights. The problems of b-balanced cuts and k-multiway separators are unified with a new problem called minimum capacity {rho}-separators. A {rho}-separator is a subset of edges whose removal partitions the vertex set into connected components such that the sum of the vertex weights in each component is at most {rho} times the weight of the graph. We present a new and simple O(log n)-approximation algorithm for minimum capacity {rho}-separators yielding an O(log n)-approximation algorithm both for b-balanced cuts and k-multiway separators. In particular, this result improves the previous best known approximation factor for k-multiway separators in undirected graphs by a factor of O(log k). We enhance these results by presenting a version of the algorithm that obtains an O(log OPT)- approximation factor. The algorithm is based on a technique called spreading metrics that enables us to formulate directly the minimum capacity {rho}-separator problem as an integer program. We also consider a generalization called the simultaneous separator problem, where the goal is to find a minimum capacity subset of edges that separates a given collection of subsets simultaneously. We extend our results to directed graphs for values of {rho} {ge} {1/2}. We conclude with an efficient algorithm for computing an optimal spreading metric for {rho}-separators. This yields more efficient algorithms for computing b-balanced cuts than were previously known.

• OSTI ID: 471721
• Report Number(s): CONF-970142--; CNN: Grant 92-00225
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DIAGRAMS
OPTIMIZATION
PARTITION