We consider the k-strong conflict-free (k-SCF) coloring of a set of points on a line with respect to a family of intervals: Each point on the line must be assigned a color so that the coloring is conflict-free in the following sense: in every interval I of the family there are at least k colors each appearing exactly once in I. We first present a polynomial time algorithm for the general problem; the algorithm has approximation ratio 2 when k = 1 and 5 - 2/k when k > 1 (our analysis is tight). In the special case of a family that contains all possible intervals on the given set of points, we show that a 2-approximation algorithm exists, for any k ≥ 1. We also show that the problem of deciding whether a given family of intervals can be 1-SCF colored with at most q colors has a quasipolynomial time algorithm. © Springer-Verlag 2012.
CITATION STYLE
Cheilaris, P., Gargano, L., Rescigno, A. A., & Smorodinsky, S. (2012). Strong conflict-free coloring for intervals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7676 LNCS, pp. 4–13). Springer Verlag. https://doi.org/10.1007/978-3-642-35261-4_4
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