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arXiv · 1705.05946

Optimal segmentation of directed graph and the minimum number of feedback arcs

Yi-Zhi Xu·Hai-Jun Zhou
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Abstract

The minimum feedback arc set problem asks to delete a minimum number of arcs (directed edges) from a digraph (directed graph) to make it free of any directed cycles. In this work we approach this fundamental cycle-constrained optimization problem by considering a generalized task of dividing the digraph into D layers of equal size. We solve the D-segmentation problem by the replica-symmetric mean field theory and belief-propagation heuristic algorithms. The minimum feedback arc density of a given random digraph ensemble is then obtained by extrapolating the theoretical results to the limit of large D. A divide-and-conquer algorithm (nested-BPR) is devised to solve the minimum feedback arc set problem with very good performance and high efficiency.

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BibTeXRIS

Yi-Zhi Xu, Hai-Jun Zhou. 2017-05-16. Optimal segmentation of directed graph and the minimum number of feedback arcs. https://doi.org/10.1007/s10955-017-1860-5

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