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

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  • Imran Khan
  • Naveed Riaz

Abstract

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.

Suggested Citation

  • Imran Khan & Naveed Riaz, 2015. "A new and fast approximation algorithm for vertex cover using a maximum independent set (VCUMI)," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(4), pages 5-18.
    • Handle: RePEc:wut:journl:v:4:y:2015:p:5-18:id:1156
    DOI: 10.5277/ord150401
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    References listed on IDEAS

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    1. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    2. Alok Singh & Ashok Kumar Gupta, 2006. "A Hybrid Heuristic For The Minimum Weight Vertex Cover Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 273-285.
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