Abstract
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.
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