Online coloring of disk graphs
Joanna Chybowska-Sok\'o{\l}, Konstanty Junosza-Szaniawski

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Optimization and Search Problems
