ISAAC 2012: Algorithms and Computation pp 4-13

# Strong Conflict-Free Coloring for Intervals

• Panagiotis Cheilaris
• Luisa Gargano
• Shakhar Smorodinsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)

## Abstract

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 $$5-\frac{2}{k}$$ 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.

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## Authors and Affiliations

• Panagiotis Cheilaris
• 1
• Luisa Gargano
• 2