A Framework for Computing Greedy Clique Cover

TL;DR

This paper introduces a new greedy framework and fixed-parameter algorithms for edge clique cover problems that incorporate graph degeneracy, demonstrating practical effectiveness and novel set theoretic concepts.

Contribution

It presents a novel greedy framework and fixed-parameter tractable algorithms for clique cover problems that leverage graph degeneracy and set theoretic concepts.

Findings

Algorithms are effective in practice.

Framework incorporates graph degeneracy.

Set theoretic approach aids computation.

Abstract

Structural parameters of graph (such as degeneracy and arboricity) had rarely been considered when designing algorithms for $\textit{(edge) clique cover}$ problems. Taking degeneracy of graph into account, we present a greedy framework and two fixed-parameter tractable algorithms for $\textit{clique cover}$ problems. We introduce a set theoretic concept and demonstrate its use in the computations of different objectives of $\textit{clique cover}$. Furthermore, we show efficacy of our algorithms in practice.