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 - 10.1007/978-3-642-35261-4_4
DO - 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 -