Conflict Packing Yield Linear Vertex-Kernels for k- Fast, k-Dense rti and a Related Problem

Abstract : We develop a technique that we call Conflict Packing in the context of kernelization. We illustrate this technique on several well-studied problems: Feedback Arc Set in Tournaments, Dense Rooted Triplet Inconsistency and Betweenness in Tournaments. For the former, one is given a tournament T = (V , A) and seeks a set of at most k arcs whose reversal in T results in an acyclic tournament. While a linear vertex-kernel is already known for this problem [6], using the Conflict Packing allows us to find a so-called safe partition, the central tool of the kernelization algorithm in [6], with simpler arguments. Regarding the Dense Rooted Triplet Inconsistency problem, one is given a set of vertices V and a dense collection R of rooted binary trees over three vertices of V and seeks a rooted tree over V containing all but at most k triplets from R. Using again the Conflict Packing, we prove that the Dense Rooted Triplet Inconsistency problem admits a linear vertex-kernel. This result improves the best known bound of O(k^2) vertices for this problem [18]. Finally, we use this technique to obtain a linear vertex-kernel for Betweenness in Tournaments, where one is given a set of vertices V and a dense collection R of betweenness triplets and seeks an ordering containing all but at most k triplets from R. To the best of our knowledge this result constitutes the first polynomial kernel for the problem.
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Communication dans un congrès
Mfcs'11: 36th International Symposium on Mathematical Foundations of Computer Science, Warsaw, Poland. Springer, pp.497-507, 2011, Lecture Notes in Computer Science
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00642335
Contributeur : Christophe Paul <>
Soumis le : jeudi 17 novembre 2011 - 20:46:55
Dernière modification le : jeudi 24 mai 2018 - 15:59:22

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  • HAL Id : lirmm-00642335, version 1

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Christophe Paul, Anthony Perez, Stéphan Thomassé. Conflict Packing Yield Linear Vertex-Kernels for k- Fast, k-Dense rti and a Related Problem. Mfcs'11: 36th International Symposium on Mathematical Foundations of Computer Science, Warsaw, Poland. Springer, pp.497-507, 2011, Lecture Notes in Computer Science. 〈lirmm-00642335〉

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