TY - GEN
T1 - Online conflict-free colorings for hypergraphs
AU - Bar-Noy, Amotz
AU - Cheilaris, Panagiotis
AU - Olonetsky, Svetlana
AU - Smorodinsky, Shakhar
PY - 2007/1/1
Y1 - 2007/1/1
N2 - We provide a framework for online conflict-free coloring (CFcoloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CF-coloring any k-degenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high probability. As a corollary, we obtain asymptotically optimal randomized algorithms for online CF-coloring some hypergraphs that arise in geometry. Our algorithm uses exponentially fewer random bits compared to previous results. We introduce deterministic online CF-coloring algorithms for points on the line with respect to intervals and for points on the plane with respect to halfplanes (or unit discs) that use ⊖(logn) colors and recolor O(n) points in total.
AB - We provide a framework for online conflict-free coloring (CFcoloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CF-coloring any k-degenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high probability. As a corollary, we obtain asymptotically optimal randomized algorithms for online CF-coloring some hypergraphs that arise in geometry. Our algorithm uses exponentially fewer random bits compared to previous results. We introduce deterministic online CF-coloring algorithms for points on the line with respect to intervals and for points on the plane with respect to halfplanes (or unit discs) that use ⊖(logn) colors and recolor O(n) points in total.
UR - http://www.scopus.com/inward/record.url?scp=38149066745&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-73420-8_21
DO - 10.1007/978-3-540-73420-8_21
M3 - Conference contribution
AN - SCOPUS:38149066745
SN - 3540734198
SN - 9783540734192
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 219
EP - 230
BT - Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PB - Springer Verlag
T2 - 34th International Colloquium on Automata, Languages and Programming, ICALP 2007
Y2 - 9 July 2007 through 13 July 2007
ER -