Muhammad Fayaz

Clever Steady Strategy Algorithm: A Simple and Efficient Approximation Algorithm for Minimum Vertex Cover Problem

This paper presents a simple and fast polynomial time algorithm, the clever, steady strategy algorithm (CSSA). The proposed algorithm consists of three stages which produces optimal or approximate vertex cover for any unknown un-weighted and undirected G = (V, E). In the first step the degree of each node of the given graph is calculated. In second step the minimum degree node(s) is find and also the adjacent nodes of minimum degree nodes are find. In the third stage the minimum degree node in all adjacent nodes of minimum degree is searched out and is selected as a candidate for MVC and all its edges are deleted. These three steps are processed repeatedly until no edge remains in the graph. The CSSA is tested on small as well as on large benchmark instances. The experimental results and comparative analysis show that the CSSA yields better and fast solution than those approximation algorithms found in literature for solving minimum vertex cover problem.

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.