Advice Complexity of the Online Vertex Coloring Problem
Sebastian Seibert, Andreas Sprock, Unger, Walter · Repository for Publications and Research Data (ETH Zurich) · 2012
We study online algorithms with advice for the problem of col oring graphs which come as input vertex by vertex. We consider the class of all 3-colorable graphs and its sub-classes of chordal and maximal outerplanar graphs, respectively. We show that, in the case of the first two classes, for coloring optimally, essentially log2 3 advice bits per vertex (bpv) are necessary and sufficient. In the case of maximal outerplanar graphs, we show a lower bound of 1.0424 bpv and an upper bound of 1.2932 bpv. Finally, we develop algorithms for 4-coloring in these graph classes. The al gorithm for 3 colorable chordal and outerplanar graphs uses 0.9865 bpv, and in case of general 3-colorable graphs, we obtain an algorithm using < 1.1583 bpv.