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.

0 Bookmarks
 · 
76 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider the k-strong conflict-free coloring of a set of points on a line with respect to a family of intervals: Each point on the line must be assigned a color so that the coloring has to be conflict-free, in the sense that in every interval I there are at least k colors each appearing exactly once in I. In this paper, we present a polynomial algorithm for the general problem; the algorithm has an approximation factor 5-2/k when k\geq2 and approximation factor 2 for k=1. In the special case the family contains all the possible intervals on the given set of points, we show that a 2 approximation algorithm exists, for any k\geq1.
    Algorithmica 05/2012; · 0.57 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A con∞ict-free coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color difierent from that of the rest of the disks that covers p. In the dynamic o†ine setting, a sequence of disks is given, we have to color the disks one-by-one according to the order of the sequence and maintain the con∞ict-free property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic o†ine setting using O(logn) colors. The algorithm is asymptotically optimal because ›(logn) colors is necessary to color some set of n unit disks for any value of n (9).
    Approximation and Online Algorithms, 6th International Workshop, WAOA 2008, Karlsruhe, Germany, September 18-19, 2008. Revised Papers; 01/2008
  • [Show abstract] [Hide abstract]
    ABSTRACT: A con∞ict-free coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color difierent from that of the rest of the disks that covers p. In the dynamic o†ine setting, a sequence of disks is given, we have to color the disks one-by-one according to the order of the sequence and maintain the con∞ict-free property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic o†ine setting using O(logn) colors. The algorithm is asymptotically optimal because ›(logn) colors is necessary to color some set of n unit disks for any value of n (8).

Full-text

Download
0 Downloads