On the Approximability of the Maximum Interval Constrained Coloring Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)


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.


Conjunctive Normal Form Discrete Tomography Coloring Requirement Variable Gadget Dynamic Program Matrix 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  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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