Improved Approximation Algorithms for Maximum Graph Partitioning Problems

Abstract Abstract. In this paper we improve the analysis of approximation algorithms based on semidefinite programming for the maximum graph partitioning problems MAX-k-CUT, MAX-k-UNCUT, MAX-k-DIRECTEDCUT, MAX-k-DIRECTED-UNCUT, MAX-k-DENSE-SUBGRAPH, and MAX-k-VERTEX-COVER. It was observed by Han, Ye, Zhang (2002) and Halperin, Zwick (2002) that a parameter-driven random hyperplane can lead to better approximation factors than obtained by Goemans and Williamson (1994). Halperin and Zwick could describe the approximation factors by a mathematical optimization problem for the above problems for k = n 2 and found a choice of parameters in a heuristic way. The innovation of this paper is twofold. First, we generalize the algorithm of Halperin and Zwick to cover all cases of k, adding some algorithmic features. The hard work is to show that this leads to a mathematical optimization problem for an optimal choice of parameters. Secondly, as a key-step of this paper we prove that a sub-optimal...

• Type: Conference
• Year: 2004
• Where: FSTTCS
• Authors: Gerold Jäger, Anand Srivastav
• Keywords: Approximation Factors, Better Approximation Factors, FSTTCS 2004, Mathematical Optimization Problem