A spectral partitioning algorithm for maximum directed cut problem
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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.
KeywordsMaximum 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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