Multicoloring of cannonball graphs

TL;DR

This paper introduces approximation algorithms for multicoloring cannonball graphs, a higher-dimensional generalization of frequency allocation problems in cellular networks, addressing complex mathematical challenges.

Contribution

It presents the first approximation algorithms for multicoloring of cannonball graphs, extending the problem to higher dimensions.

Findings

Developed the first approximation algorithms for cannonball graphs

Extended multicoloring problem to higher dimensions

Addressed mathematical challenges in frequency allocation modeling

Abstract

The frequency allocation problem that appeared in the design of cellular telephone networks can be regarded as a multicoloring problem on a weighted hexagonal graph, which opened some still interesting mathematical problems. We generalize the multicoloring problem into higher dimension and present the first \jz{approximation} algorithms for multicoloring of so called cannonball graphs.