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Fast Local Search Algorithm for Weighted Feedback Arc Set in Tournaments

Last modified: 2010-07-03

#### Abstract

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solutionto an instance of Weighted Feedback Arc Set in Tournaments. More precisely,given an arc weighted tournament

*T*on*n*vertices and a feedback arc set*F*(a set of arcs whose deletion from*T*turns it into a directed acyclic graph), our algorithm decides in time*O(2*log^{o(k)}n*n)*if there is a feedback arc set of smaller weight and that differs from F in at most k arcs. To our knowledge this is the first algorithm searching the*k*-exchange neighborhood of an NP-complete problem that runs in (parameterized) subexponential time. Using this local search algorithm for Weighted Feedback Arc Set in Tournaments, we obtain subexponential time algorithms for a local search variant of Kemeny Ranking — a problem in social choice theory and of One-Sided Cross Minimization — a problem in graph drawing.
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