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Approximation Algorithm for MAX DICUT with Given Sizes of Parts

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Abstract

Given a directed graph G and an edge weight function w : A(G) → R + the maximum directed cut problem (MAX DICUT) is that of finding a directed cut δ(S) with maximum total weight. We consider a version of MAX DICUT — MAX DICUT with given sizes of parts or MAX DICUT WITH GSP — whose instance is that of MAX DICUT plus a positive integer k, and it is required to find a directed cut δ(S) having maximum weight over all cuts δ(S) with |S|=k. We present an approximation algorithm for this problem which is based on semidefinite programming (SDP) relaxation. The algorithm achieves the presently best performance guarantee for a range of k.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Dachuan Xu

  2. WHQKB, Research and Development, United Airlines, Elk Grove Township, IL, 60007, USA

    Guanghui Liu

Authors
  1. Dachuan Xu
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  2. Guanghui Liu
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Corresponding author

Correspondence to Dachuan Xu.

Additional information

Supported by K. C. Wong Education Foundation of Hong Kong, Chinese NSF (Grant No. 19731001) and National 973 Information Technology and High-Performance Software Program of China (Grant No. G1998030401)

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Xu, D., Liu, G. Approximation Algorithm for MAX DICUT with Given Sizes of Parts. Acta Mathematicae Applicatae Sinica, English Series 19, 289–296 (2003). https://doi.org/10.1007/s10255-003-0104-4

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  • DOI: https://doi.org/10.1007/s10255-003-0104-4

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