Algorithms for Graph Partitioning on the Planted Partition Model

  • Anne Condon
  • Richard M. Karp
Conference paper

DOI: 10.1007/978-3-540-48413-4_23

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1671)
Cite this paper as:
Condon A., Karp R.M. (1999) Algorithms for Graph Partitioning on the Planted Partition Model. In: Hochbaum D.S., Jansen K., Rolim J.D.P., Sinclair A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg

Abstract

The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups.

We present a simple, linear-time algorithm for the graph l-partition problem and analyze it on a random “planted l-partition” model. In this model, the n nodes of a graph are partitioned into l groups, each of size n/l; two nodes in the same group are connected by an edge with some probability p, and two nodes in different groups are connected by an edge with some probability r < p. We show that if pr > n − − 1/2 + ε for some constant ε, then the algorithm finds the optimal partition with probability \(1 - \exp( -n^{\theta(\epsilon)})\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Anne Condon
    • 1
  • Richard M. Karp
    • 2
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  2. 2.Department of Computer Science and EngineeringUniversity of WashingtonSeattleUSA

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