Designing Parallel Graph Coloring Algorithm - A Research Perspective

Graph Coloring Problem is a well know NP-Hard problem. In vertex coloring problem all vertices of any graph must be colored in such a way that no two adjacent vertices colored with same color. In this research work two different algorithms are proposed to solve vertex coloring problems, Edge Cover based Graph Coloring Algorithm (ECGCA) and Tree Data Structure based Graph Coloring Algorithm (TGCA). One parallel version of ECGCA, Parallel Edge Cover based Graph Coloring Algorithm (PECGCA) is also proposed. ECGCA algorithm is based on finding vertex sets using edge cover method. In this research work implementation prospective of algorithm are also covered. Implemented algorithm is tested on various graph instances of DIMACS standards dataset. Algorithm execution time and number of colored required to color graph are compared with some other well know Graph Coloring Algorithms. Variation in time complexity with reference to increasing in number of vertices, number of edges and average degree of graph is also analyzed in this research work. In PECGCA enhanced parallel edge cover based graph coloring algorithm by incorporating parallel computing aspects in algorithm is introduced.