Abstract
We provide a framework for online conflict-free coloring (CF-coloring) 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 logn) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k logk logn) 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 Θ(logn) colors and recolor O(n) points in total.
The first two authors are partially supported by the CUNY Collaborative Incentive Research Grants Program Round 11 (2004–2006).
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Bar-Noy, A., Cheilaris, P., Olonetsky, S., Smorodinsky, S. (2007). Online Conflict-Free Colorings for Hypergraphs. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_21
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DOI: https://doi.org/10.1007/978-3-540-73420-8_21
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