Computing Clique Cover with Structural Parameterization

TL;DR

This paper develops fixed-parameter tractable algorithms for various clique cover problems in graphs, leveraging structural parameters and a novel set-based framework to achieve significant improvements in computational efficiency.

Contribution

It introduces a new set representation framework for clique cover problems and provides multiple algorithms with exponential to double exponential speedups.

Findings

New algorithms with exponential to double exponential improvements in running time

Framework applicable to various clique cover objectives

Enhanced understanding of structural parameters in graph algorithms

Abstract

An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable algorithms for a number of clique cover problems. Using a set representation of graph, we introduce a framework for computing clique cover with different objectives. We demonstrate use of the framework for a variety of clique cover problems. Our results include a number of new algorithms with exponential to double exponential improvements in the running time.