Abstract
Given a directed network G(N;A), the minimum feedback arc set problem is to find a minimal weighted subset of arcs A' ⊂ A so that G(N;A\\A′) is acyclic. We first provide a mixed 0-1 integer programming formulation whose LP relaxation can be solved by a strongly polynomial algorithm of complexity O(|N|3 log |N|). An enumerative framework is provided which makes use of this relaxation repeatedly. We also provide a result which gives rise to a heuristic algorithm.
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