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Canzar, Stefan; Elbassioni, Khaled; Elmasry, Amr; Raman, Rajiv (2018): On the approximability of the maximum interval constrained coloring problem. In: Discrete Optimization, Vol. 27: pp. 57-72
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In the MAXIMUM INTERVAL CONSTRAINED COLORING problem, we are given a set of vertices and 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 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(root vertical bar OPT vertical bar)-approximation algorithm, where OPT is the smallest cardinality maximum-weight solution. We show further that, even for k = 2, the problem remains APX-hard.