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 - פרסום מוקדם
BT - Conflict-free coloring with respect to a subset of intervals
PB - arXiv:1204.6422 [math.CO]
ER -