On the Approximability of the Maximum Interval Constrained Coloring Problem

  • Stefan Canzar
  • Khaled Elbassioni
  • Amr Elmasry
  • Rajiv Raman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)

Abstract

In the Maximum Interval Constrained Coloring problem, we are given a set of intervals on a line and a k-dimensional requirement vector for each interval, specifying how many vertices of each of k colors should appear in the interval. The objective is to color the vertices of the line with k colors so as to maximize the total weight of intervals for which the requirement is satisfied. This \(\mathcal{NP}\)-hard combinatorial problem arises in the interpretation of data on protein structure emanating from experiments based on hydrogen/deuterium exchange and mass spectrometry. For constant k, we give a factor \(O(\sqrt{|{\textsc{Opt}}|})\)-approximation algorithm, where Opt is the smallest-cardinality maximum-weight solution. We show further that, even for k = 2, the problem remains APX-hard.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefan Canzar
    • 1
  • Khaled Elbassioni
    • 2
  • Amr Elmasry
    • 2
    • 3
  • Rajiv Raman
    • 4
  1. 1.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Datalogisk InstitutUniversity of CopenhagenCopenhagenDenmark
  4. 4.DIMAP and Department of Computer ScienceUniversity of WarwickUK

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