Abstract
In the k-Feedback Arc/Vertex Set problem we are given a directed graph D and a positive integer k and the objective is to check whether it is possible to delete at most k arcs/vertices from D to make it acyclic. Dom et al. (J. Discrete Algorithm 8(1):76–86, 2010) initiated a study of the Feedback Arc Set problem on bipartite tournaments (k-FASBT) in the realm of parameterized complexity. They showed that k-FASBT can be solved in time O(3.373k n 6) on bipartite tournaments having n vertices. However, until now there was no known polynomial sized problem kernel for k-FASBT. In this paper we obtain a cubic vertex kernel for k-FASBT. This completes the kernelization picture for the Feedback Arc/Vertex Set problem on tournaments and bipartite tournaments, as for all other problems polynomial kernels were known before. We obtain our kernel using a non-trivial application of “independent modules” which could be of independent interest.
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A preliminary version of this work [26] appeared in the proceedings of The 22nd International Symposium on Algorithms and Computation (ISAAC 2011).
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Misra, P., Raman, V., Ramanujan, M.S. et al. A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments. Theory Comput Syst 53, 609–620 (2013). https://doi.org/10.1007/s00224-013-9453-4
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DOI: https://doi.org/10.1007/s00224-013-9453-4