Abstract

(i) We provide a framework for online conflict-free coloring (CF-coloring) 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 probability. (ii) We show a deterministic online CF-coloring algorithm for points on the line with respect to intervals that uses Θ(log n) colors by allowing at most one recoloring operation at any given insertion step. We also show a deterministic online CF-coloring algorithm for points in plane with respect to halfplanes that uses Θ(log n) colors and recolors O(n) points during the run. As a corollary of (i), we obtain asymptotically optimal randomized algorithms for online CF-coloring some hypergraphs that arise in geometry and model an important version of the frequency assignment task for cellular networks. For example, hypergraphs that are induced by n points on a line with respect to intervals and also for n points in the plane with

Citations