A contraction algorithm for finding small cycle cutsets
Journal of Algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Computing Minimum Feedback Vertex Sets by Contraction Operations and its Applications on CAD
ICCD '99 Proceedings of the 1999 IEEE International Conference on Computer Design
Approximation algorithms for the loop cutset problem
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
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The feedback vertex set problem (FVSP) consists in making a given directed graph acyclic by removing as few vertices as possible. In spite of the importance of this NP-hard problem, no local search approach had been proposed so far for tackling it. Building on a property of acyclic graphs, we suggest in this paper a new representation of the solutions of the FVSP (feedback sets). Thanks to this solution representation, we are able to design a local transformation (equivalent to a neighborhood) that changes a feedback set into a new one. Based on this neighborhood, we have developed a simulated annealing algorithm for the FVSP. Our experiments show that our algorithm outperforms the best existing heuristic, namely the greedy adaptive search procedure by Pardalos et al.