TY - GEN

T1 - Strong conflict-free coloring for intervals

AU - Cheilaris, Panagiotis

AU - Gargano, Luisa

AU - Rescigno, Adele A.

AU - Smorodinsky, Shakhar

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84871564924&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-642-35261-4_4

DO - https://doi.org/10.1007/978-3-642-35261-4_4

M3 - Conference contribution

SN - 9783642352607

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 4

EP - 13

BT - Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings

PB - Springer Verlag

T2 - 23rd International Symposium on Algorithms and Computation, ISAAC 2012

Y2 - 19 December 2012 through 21 December 2012

ER -