A new and fast approximation algorithm for vertex cover using a maximum independent set (VCUMI)

• Authors: KHAN Imran , RIAZ Naveed
• Languages of publication: EN

Abstracts

EN

The importance of non-deterministic polynomial (NP) problems in real world scenarios has compelled researchers to consider simple ways of finding approximate solutions to these problems in polynomial time. Minimum vertex cover is an NP complete problem, where the objective is to cover all the edges in a graph with the minimal number of vertices possible. The maximal independent set and maximal clique problems also belong to the same class. An important property that we have ana-lyzed while considering various approaches to find approximate solutions to the minimum vertex cover problem (MVC) is that solving MVC directly can result in a bigger error ratio. We propose a new approximation algorithm for the minimum vertex cover problem called vertex cover using a maximum independent set (VCUMI). This algorithm works by removing the nodes of a maximum independent set until the graph is an approximate solution of MVC. Based on empirical results, it can be stated that VCUMI outperforms all competing algorithms presented in the literature. Based on all the benchmarks used, VCUMI achieved the worst case error ratio of 1.033, while VSA, MDG and NOVAC-1 gave the worst error ratios of 1.583, 1.107 and 1.04, respectively.

Keywords

EN

non-deterministic polynomial; vertex coverindependent set benchmark; error ratio

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2015
• Volume: 25
• Issue: 4
• Pages: 5-18

Contributors

author

KHAN Imran

• Gran Sasso Science Institute, viale Francesco Crispi, 7 67100 L’Aquila (AQ), ITALY

author

RIAZ Naveed

• College of Computer Science and IT, University of Dammam, Saudi Arabia

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Identifiers

DOI

10.5277/ord150401