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.
Part of the work was done while the first, third and forth authors were members of Max-Planck Institute. A. Elmasry is on leave from Alexandria University of Egypt. R. Raman’s research is supported by the Centre for Discrete Mathematics and its Applications (DIMAP) at University of Warwick, EPSRC award EP/D063191/1.
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Canzar, S., Elbassioni, K., Elmasry, A., Raman, R. (2010). On the Approximability of the Maximum Interval Constrained Coloring Problem. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_15
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DOI: https://doi.org/10.1007/978-3-642-17514-5_15
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