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Online Conflict-Free Colorings for Hypergraphs

  • Amotz Bar-Noy
  • Panagiotis Cheilaris
  • Svetlana Olonetsky
  • Shakhar Smorodinsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

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.

Keywords

Convex Hull Online Algorithm Simple Graph Deterministic Algorithm Frequency Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Amotz Bar-Noy
    • 1
  • Panagiotis Cheilaris
    • 1
    • 2
    • 3
  • Svetlana Olonetsky
    • 4
  • Shakhar Smorodinsky
    • 5
  1. 1.Brooklyn College 
  2. 2.The Graduate Center, City University of New York 
  3. 3.School of ECE, National Technical University of Athens 
  4. 4.Tel-Aviv University 
  5. 5.Courant Institute, New York University 

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