Approximation Algorithms for MAX-BISECTION on Low Degree Regular Graphs

Article type: Research Article

Authors: Karpinski, Marek | Kowaluk, Miroslaw | Lingas, Andrzej

Affiliations: Department of Computer Science, University of Bonn, Bonn, Germany | Institute of Informatics, Warsaw University, Banacha 2, Warsaw, Poland | Department of Computer Science, Lund University, 22100 Lund, Sweden

Abstract: The max-bisection problem is to find a partition of the vertices of a graph into two equal size subsets that maximizes the number of edges with endpoints in both subsets. We obtain new improved approximation ratios for the max-bisection problem on the low degree k-regular graphs for 3≤k≤8, by deriving some improved transformations from a maximum cut into a maximum bisection. In the case of three regular graphs we obtain an approximation ratio of 0.854, and in the case of four and five regular graphs, approximation ratios of 0.805, and 0.812, respectively.

Keywords: graph bisection, approximation algorithms, regular graphs

Journal: Fundamenta Informaticae, vol. 62, no. 3-4, pp. 369-375, 2004