Graph unique-maximum and conflict-free colorings

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چکیده

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Graph Unique-Maximum and Conflict-Free Colorings

We investigate the relationship between two kinds of vertex colorings of graphs: uniquemaximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color appears only once. In a conflict-free coloring, in every path of the graph there is a color that appears only once. We also study computational complexity aspec...

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Motivated by a frequency assignment problem in cellular telephone networks, Even et al. studied the following question. Given a set P of n points in general position in the plane, what is the smallest number of colors in a coloring of the elements of P with the property that any closed disk D with D ∩ P 6= ∅ has an element whose color is not assigned to any other element of D ∩ P . We refer to ...

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Background. Consider a cellular network consisting of a set of base stations, where the signal from a given base station can be received by clients within a certain distance from the base station. In general, these regions will overlap. For a client, this may lead to interference of the signals. Thus one would like to assign frequencies to the base stations such that for any client within reach...

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Conflict-free colorings of graphs and hypergraphs

A coloring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of “unique” color that does not get repeated in E. The smallest number of colors required for such a coloring is called the conflict-free chromatic number of H, and is denoted by χCF(H). This parameter was first introduced by Even et al. (FOCS 2002) in a geometric setting, in connecti...

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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 log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high p...

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ژورنال

عنوان ژورنال: Journal of Discrete Algorithms

سال: 2011

ISSN: 1570-8667

DOI: 10.1016/j.jda.2011.03.005