TY - UNPB

T1 - Conflict-free coloring with respect to a subset of intervals

AU - Cheilaris, Panagiotis

AU - Smorodinsky, Shakhar

PY - 2012

Y1 - 2012

N2 - Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S \in E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The discrete interval hypergraph Hn is the hypergraph with vertex set {1,...,n} and hyperedge set the family of all subsets of consecutive integers in {1,...,n}. We provide a polynomial time algorithm for conflict-free coloring any subhypergraph of Hn, we show that the algorithm has approximation ratio 2, and we prove that our analysis is tight, i.e., there is a subhypergraph for which the algorithm computes a solution which uses twice the number of colors of the optimal solution. We also show that the problem of deciding whether a given subhypergraph of Hn can be colored with at most k colors has a quasipolynomial time algorithm.

AB - Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S \in E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The discrete interval hypergraph Hn is the hypergraph with vertex set {1,...,n} and hyperedge set the family of all subsets of consecutive integers in {1,...,n}. We provide a polynomial time algorithm for conflict-free coloring any subhypergraph of Hn, we show that the algorithm has approximation ratio 2, and we prove that our analysis is tight, i.e., there is a subhypergraph for which the algorithm computes a solution which uses twice the number of colors of the optimal solution. We also show that the problem of deciding whether a given subhypergraph of Hn can be colored with at most k colors has a quasipolynomial time algorithm.

KW - math.CO

KW - cs.DM

KW - cs.DS

M3 - ???researchoutput.researchoutputtypes.workingpaper.preprint???

BT - Conflict-free coloring with respect to a subset of intervals

PB - arXiv:1204.6422 [math.CO]

ER -