## 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 approximation algorithm for the general problem; the algorithm has approximation ratio 2 when k=1 and 5-2/k when k ≥ 2. 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 provide, in case k = O(polylog(n)), a quasipolynomial time algorithm to decide the existence of a k-SCF coloring that uses at most q colors.

Original language | English |
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Pages (from-to) | 732-749 |

Number of pages | 18 |

Journal | Algorithmica |

Volume | 70 |

Issue number | 4 |

DOIs | |

State | Published - 25 Oct 2014 |

## Keywords

- Conflict-free coloring
- Interval hypergraph
- Wireless networks

## ASJC Scopus subject areas

- Computer Science (all)
- Computer Science Applications
- Applied Mathematics