Online Multi-Coloring with Advice

TL;DR

This paper investigates online multi-coloring in cellular network models, providing tight bounds for paths and hexagonal graphs, and explores the role of advice in improving online algorithms.

Contribution

It offers nearly tight upper and lower bounds for online multi-coloring on paths and hexagonal graphs, incorporating advice to enhance algorithm performance.

Findings

Established tight bounds for paths and hexagonal graphs.

Advice improves online coloring efficiency in cellular network models.

Results applicable to bipartite graphs due to similar properties.

Abstract

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.