A Simple, Fast and Near Optimal Approximation Algorithm for Optimization of Un-Weighted Minimum Vertex Cover

This paper presents a simple and efficient near optimal algorithm, named Maximum Adjacent Minimum degree Algorithm (MAMA) for optimization of minimum vertex cover problem. The proposed algorithm at each step add that maximum degree vertex which is adjacent to minimum degree vertex. The computational complexity and optimality comparison are carried with other state of the art algorithms on small benchmark instances as well as on large benchmark instances to check the efficiency of the proposed algorithm. The proposed algorithm outperforms the other well-known algorithm and returns near optimal result in quick time.

[1]  Egon Balas,et al.  Weighted and unweighted maximum clique algorithms with upper bounds from fractional coloring , 1996, Algorithmica.

[2]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[3]  Malte Helmert,et al.  A Stochastic Local Search Approach to Vertex Cover , 2007, KI.

[4]  S. Balaji,et al.  Optimization of Unweighted Minimum Vertex Cover , 2010 .

[5]  Gerhard J. Woeginger,et al.  Exact Algorithms for NP-Hard Problems: A Survey , 2001, Combinatorial Optimization.

[6]  Giorgio Gambosi,et al.  Complexity and approximation: combinatorial optimization problems and their approximability properties , 1999 .

[7]  Irit Dinur,et al.  The importance of being biased , 2002, STOC '02.

[8]  P. Pardalos,et al.  An exact algorithm for the maximum clique problem , 1990 .

[9]  Alexander K. Hartmann,et al.  The number of guards needed by a museum: A phase transition in vertex covering of random graphs , 2000, Physical review letters.

[10]  Kenneth L. Clarkson,et al.  A Modification of the Greedy Algorithm for Vertex Cover , 1983, Inf. Process. Lett..

[11]  Muhammad Fayaz,et al.  Clever Steady Strategy Algorithm: A Simple and Efficient Approximation Algorithm for Minimum Vertex Cover Problem , 2015, 2015 13th International Conference on Frontiers of Information Technology (FIT).

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Dorit S. Hochba,et al.  Approximation Algorithms for NP-Hard Problems , 1997, SIGA.