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


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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Available from: Amotz Bar-Noy, Mar 29, 2015
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    • "Conflict–free coloring in the case of the complete interval hypergraph has been first studied by Even et al. in [14]; they gave an algorithm showing that the problem can be optimally solved by using ⌊log n⌋ + 1 colors. The on–line version of the CF coloring problem for complete interval hypergraphs, where points arrive one by one and the coloring needs to remain CF all the time, has been subsequently considered in [5], [6], [7], [10], [11]. "
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