A spectral partitioning algorithm for maximum directed cut problem

  • Zhenning Zhang
  • Donglei Du
  • Chenchen Wu
  • Dachuan Xu
  • Dongmei ZhangEmail author


We investigate the maximum directed cut (MaxDC) problem by designing a spectral partitioning algorithm. Given a directed graph with nonnegative arc weights, we wish to obtain a bipartition of the vertices such that the total weight of the directed cut arcs is maximized. Relaxing the MaxDC problem as a quadratic program allows us to explore combinatorial properties of the optimal solution, leading to a 0.272-approximation algorithm via the technique of spectral partitioning rounding.


Maximum directed cut Spectral graph theory Spectral partitioning rounding Approximation algorithm 



The first author is supported by Beijing Excellent Talents Funding (No. 201400 0020124G046), and General Science and Technology Project of Beijing Municipal Education Commission (No. KM201810005006). The second author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 06446, and NSFC (Nos. 11771386 and 11728104). The third author’s research is supported by NSFC (No. 11501412). The fourth author’s research is supported by NSFC (Nos. 11531014 and 11871081). The fifth author is supported by Higher Educational Science and Technology Program of Shandong Province (No. J15LN22).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Zhenning Zhang
    • 1
  • Donglei Du
    • 2
  • Chenchen Wu
    • 3
  • Dachuan Xu
    • 1
  • Dongmei Zhang
    • 4
    Email author
  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.Faculty of Business AdministrationUniversity of New BrunswickFrederictonCanada
  3. 3.College of ScienceTianjin University of TechnologyTianjinPeople’s Republic of China
  4. 4.School of Computer Science and TechnologyShandong Jianzhu UniversityJinanPeople’s Republic of China

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