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Communication Dans Un Congrès Année : 2011

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

Résumé

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.

Dates et versions

lirmm-00642335 , version 1 (17-11-2011)

Identifiants

Citer

Christophe Paul, Anthony Perez, Stéphan Thomassé. Conflict Packing Yield Linear Vertex-Kernels for k- Fast, $k-Dense$ RTI and a Related Problem. 36th International Symposium on Mathematical Foundations of Computer Science (MFCS 2011), Aug 2011, Warsaw, Poland. pp.497-507, ⟨10.1007/978-3-642-22993-0_45⟩. ⟨lirmm-00642335⟩
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