Approximate Methods for Minimum Vertex Cover Fail to Provide Optimal Results on Small Graph Instances: A Review

Abstract

In this paper, a detailed literature review and comparative analysis, based on simplicity, efficiency and the run-time complexity of some well known approximation algorithms for Minimum Vertex Cover (MVC) problem have been carried out. The key contribution of this paper is the provision of small benchmark graphs on which the given approximation algorithms fail to provide optimal results. The small benchmark graphs will help the researchers to evaluate efficient approximation algorithms. Generally, different terminologies and different styles have been adopted for writing pseudo code for different algorithms. To avoid such kind of difficulties, a uniform set of terminologies and pseudo code for each algorithm is provided in this paper, which will help researchers to easily understand the approximation algorithm for Minimum Vertex Cover (MVC) problem.