Abstract
The aim of the vertex clique covering problem (CCP) is to cover the vertices of a graph with as few cliques as possible. We analyse the iterated greedy (IG) algorithm for CCP, which was previously shown to provide strong empirical results for real-world networks. It is demonstrated how the techniques of analysis for randomised search heuristics can be applied to IG, and several practically relevant results are obtained. We show that for triangle-free graphs, IG solves CCP optimally in expected polynomial time. Secondly, we show that IG finds the optimum for CCP in a specific case of sparse random graphs in expected polynomial time with high probability. For Barabási-Albert model of scale-free networks, which is a canonical model explaining the growth of social, biological or computer networks, we obtain that IG obtains an asymptotically optimal approximation in polynomial time in expectation. Last but not least, we propose a slightly modified variant of IG, which guarantees expected polynomial-time convergence to the optimum for graphs with non-overlapping triangles.
Highlights
This paper is dedicated to an analytical study of an iterated greedy (IG) heuristic for the vertex clique covering problem (CCP) in several practically relevant classes of graphs, including triangle-free graphs, sparse random graphs and models of complexPreprint of an article for the Computing and Informatics journal .David Chalupa, Jir ́ı Pospıchal networks
We presented an analysis of an iterated greedy (IG) heuristic for the vertex clique covering problem (CCP) in several practically relevant graph classes
As our analytical results indicate, IG can be viewed as a variant of local search, with non-trivial methods needed to quantify the convergence and runtime properties of this randomised search heuristic
Summary
This paper is dedicated to an analytical study of an iterated greedy (IG) heuristic for the vertex clique covering problem (CCP) in several practically relevant classes of graphs, including triangle-free graphs, sparse random graphs and models of complex. To the research on other randomised search heuristics [32], we obtain that IG mimics the behaviour of classical algorithms to some extent, provably finding optimal or asymptotically optimal solutions in polynomial time for several practically relevant graph classes.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
