A Kernel for Convex Recoloring of Weighted Forests

  • Hans L. Bodlaender
  • Marc Comas
Conference paper

DOI: 10.1007/978-3-642-11266-9_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5901)
Cite this paper as:
Bodlaender H.L., Comas M. (2010) A Kernel for Convex Recoloring of Weighted Forests. In: van Leeuwen J., Muscholl A., Peleg D., Pokorný J., Rumpe B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg

Abstract

In this paper, we show that the following problem has a kernel of quadratic size: given is a tree T whose vertices have been assigned colors and a non-negative integer weight, and given is an integer k. In a recoloring, the color of some vertices is changed. We are looking for a recoloring such that each color class induces a subtree of T and such that the total weight of all recolored vertices is at most k. Our result generalizes a result by Bodlaender et al. [3] who give quadratic size kernel for the case that all vertices have unit weight.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Marc Comas
    • 2
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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