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International Conference on Combinatorial Optimization and Applications

COCOA 2009: Combinatorial Optimization and Applications pp 219–230Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5573))

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.

This work is supported by National Natural Science Foundations of China, No. 10671152.

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Author information

Authors and Affiliations

  1. School of Finance, Jiangxi University of Finance & Economics, Nanchang, 330013, China

    Ai-fan Ling

Authors
  1. Ai-fan Ling
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 800 West Campbell Road, TX 75080-3021, Richardson, USA

    Ding-Zhu Du

  2. Chinese Academy of Sciences, Institute of Applied Mathematics, Zhong Guan Cun Dong Lu 55, 100190, Beijing, P. R. China

    Xiaodong Hu

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, FL 32611-6595, Gainesville, USA

    Panos M. Pardalos

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© 2009 Springer-Verlag Berlin Heidelberg

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Ling, Af. (2009). Approximation Algorithms for Max 3-Section Using Complex Semidefinite Programming Relaxation. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_20

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  • DOI: https://doi.org/10.1007/978-3-642-02026-1_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02025-4

  • Online ISBN: 978-3-642-02026-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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