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Local Search Approximation Algorithms for the Complement of the Min-$k$-Cut Problems

Wenxing Zhu (wxzhu2000***at***yahoo.com.cn)
Chuanyin Guo (wxzhu2000***at***yahoo.com.cn)

Abstract: Min-$k$-cut is the problem of partitioning vertices of a given graph or hypergraph into $k$ subsets such that the total weight of edges or hyperedges crossing different subsets is minimized. For the capacitated min-$k$-cut problem, each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that minimizes the sum of edge weights on all pairs of vertices that lie in different subsets. The min-$k$-cut problem is NP-hard for $k \geq 3$, and the capacitated min-$k$-cut problem is also NP-hard for $k \geq 2$. Min-$k$-cut has numerous applications, for example, VLSI circuit partitioning, which is a key step in VLSI CAD. Although many heuristics have been proposed for min-$k$-cut problems, there are few approximation results of min-$k$-cut problems. We study the equivalent complement problem of the min-$k$-cut problem and extend the method proposed in \cite{gauer} to present deterministic local search approximation algorithms for the complement problem of the min-$k$-cut problem, and the complement problem of the capacitated min-$k$-cut problem on graph with performance ratio $\frac{1}{k}$.

Keywords: min-$k$-cut, approximation algorithm, local search.

Category 1: Combinatorial Optimization (Approximation Algorithms )

Citation: Research Report, Fuzhou University, CHINA. 2010.6.30

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Entry Submitted: 07/07/2010
Entry Accepted: 07/08/2010
Entry Last Modified: 07/09/2010

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