Online coloring of disk graphs

TL;DR

This paper introduces improved online algorithms for coloring intersection graphs of disks with bounded diameter, leveraging geometric representations and novel partitioning techniques to achieve better competitive ratios.

Contribution

It presents new online coloring algorithms with enhanced competitive ratios for disk graphs, utilizing geometric partitioning and extending to other shapes and labeling problems.

Findings

Algorithms outperform previous methods in competitive ratio

Techniques applicable to other planar shapes

Extension to online L(2,1)-labeling

Abstract

In this paper, we give a family of online algorithms for the classical coloring problem of intersection graphs of discs with bounded diameter. Our algorithms make use of a geometric representation of such graphs and are inspired by an algorithm of Fiala et al., but have better competitive ratios. The improvement comes from using two techniques of partitioning the set of vertices before coloring them. One of whichis an application of a b-fold coloring of the plane. The method is more general and we show how it can be applied to coloring other shapes on the plane as well as adjust it for online L(2, 1)-labeling.