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

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 nonnegative 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 ≥ 3, and the capacitated min-k-cut problem is also NP-hard for k ≥ 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, which attempts to maximize the total weight of edges in every subset. We extend the method proposed in [15] 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 1 k .