Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadatas

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00642335
Contributor : Christophe Paul <>
Submitted on : Thursday, November 17, 2011 - 8:46:55 PM
Last modification on : Wednesday, August 28, 2019 - 1:34:00 PM

Identifiers

  • HAL Id : lirmm-00642335, version 1

Collections

Citation

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. pp.497-507. ⟨lirmm-00642335⟩

Share

Metrics

Record views

156