Deconstructing intractability-A multivariate complexity analysis of interval constrained coloring

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Abstract

The NP-hard Interval Constrained Coloring (ICC) problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments. Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to be used for its elements), one asks whether there is a "consistent" coloring for all integer points from {1,...,n} that complies with the constraints specified by the color multisets. We thoroughly analyze a known NP-hardness proof for ICC. In this way, we identify numerous parameters that naturally occur in ICC and strongly influence its practical solvability. Accordingly, we present several positive (fixed-parameter) tractability results exploiting various parameterizations. We substantiate the usefulness of this "multivariate algorithmics approach" by presenting experimental results with real-world data. © 2010 Elsevier B.V. All rights reserved.

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Komusiewicz, C., Niedermeier, R., & Uhlmann, J. (2011). Deconstructing intractability-A multivariate complexity analysis of interval constrained coloring. In Journal of Discrete Algorithms (Vol. 9, pp. 137–151). https://doi.org/10.1016/j.jda.2010.07.003

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