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An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding

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Abstract

Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem. We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.

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Acknowledgments

The authors would like to thank Peng Zhang and Yishui Wang for their helpful comments on an earlier version of this paper. This work was partially done while the first author was a visiting doctorate student at the Department of Applied Mathematics, Beijing University of Technology and supported in part by NSF of China (No. 11071268). The research of the second author is supported by NSF of China (No. 11371001) and Collaborative Innovation Center on Beijing Society-building and Social Governance. The third author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106. A preliminary version of the paper appeared in Proceedings of the 20th Annual International Computing and Combinatorics Conference (COCOON’14), Atlanta, Georgia, USA, 2014.

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Authors and Affiliations

  1. College of Science, Tianjin University of Technology, Xiqing District, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

  2. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Dachuan Xu & Wenqing Xu

  3. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  4. Department of Mathematics and Statistics, California State University, Long Beach, CA, 90840, USA

    Wenqing Xu

Authors
  1. Chenchen Wu
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Wenqing Xu
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Correspondence to Dachuan Xu.

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Wu, C., Xu, D., Du, D. et al. An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding. J Comb Optim 32, 1017–1035 (2016). https://doi.org/10.1007/s10878-015-9880-z

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