Conference Paper

Online Conflict-Free Colorings for Hypergraphs.

DOI: 10.1007/978-3-540-73420-8_21 Conference: Automata, Languages and Programming, 34th International Colloquium, ICALP 2007, Wroclaw, Poland, July 9-13, 2007, Proceedings
Source: DBLP

ABSTRACT We provide a framework for online con∞ict-free coloring (CF-coloring) of any hyper- graph. We use this framework to obtain an e-cient randomized online algorithm for CF-coloring any k-degenerate hypergraph. Our algorithm uses O(klogn) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our al- gorithm uses O(klogklogn) 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.

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