Approximation Algorithms for Max 3-Section Using Complex Semidefinite Programming Relaxation

Authors:
Ai-Fan Ling
Affiliations:
School of Finance, Jiangxi University of Finance & Economics, Nanchang, China 330013
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

We present an approximation algorithm for the Max 3-section problem which divides a weighted graph into 3 parts of equal size so as to maximize the weight of the edges connecting different parts. The algorithm is based on a complex semidefinite programming and can in some sense be viewed as a generalization of the approximation algorithm proposed by Ye [17] for the Max Bisection problem. Our algorithm can hit the 2/3 bound and has approximate ratio 0.6733 for Max 3-section that sightly improves the 2/3 bound obtained by Andersson [1] and Gaur [8], respectively.