Conflict-Free Coloring and its Applications

TL;DR

This paper surveys conflict-free coloring of hypergraphs, a concept extending classical coloring, with applications in wireless communication, sensor networks, and RFID, highlighting its combinatorial and algorithmic aspects.

Contribution

It provides a comprehensive overview of conflict-free coloring, summarizing recent research, and discussing its theoretical foundations and practical applications.

Findings

Summarizes key combinatorial properties of conflict-free coloring.

Reviews algorithms for conflict-free coloring in various contexts.

Highlights applications in wireless communication and sensor networks.

Abstract

Let $H=(V,E)$ be a hypergraph. A {\em conflict-free} coloring of $H$ is an assignment of colors to $V$ such that in each hyperedge $e \in E$ there is at least one uniquely-colored vertex. This notion is an extension of the classical graph coloring. Such colorings arise in the context of frequency assignment to cellular antennae, in battery consumption aspects of sensor networks, in RFID protocols and several other fields, and has been the focus of many recent research papers. In this paper, we survey this notion and its combinatorial and algorithmic aspects.