Indian Journal of Science and Technology

Abstract

Objective: To improve the Edge Cover based Graph Coloring Algorithm (ECGCA) using independent set by incorporating parallel computing aspects in algorithm. Finding optimum time complexity is one of the main objectives of this paper. Methods/Statistical Analysis: This paper introduced some modification in ECGCA. Algorithm is implemented and tested using Java programming language. Java multithreading concept is used to achieve parallel computing in algorithm. DIMACS graph instances are used to test algorithm. Finding: Algorithm is tested on more than 75 DIMACS graph instances. To analyze the time complexity, execution time of algorithm in seconds is calculated by program. Algorithm is tested on different DIMACS graph instances. Test data is analyze in this paper and found that proposed algorithm executed in optimum time for large graphs. This paper also compared parallel algorithm and found that proposed parallel algorithm is less time complex than sequential algorithm. Most of the exact graph coloring algorithms are not suitable for large graph (more than 100 vertices) but proposed algorithm is tested on many large graphs and high execution success rate of algorithm is achieved. Application: This paper shows the experimental results of different type of application data. It means this algorithm can be used for maximum types of applications.

Keywords: Edge Cover, Graph Coloring, Independent Set, Multithreading, Parallel Computing, Vertex Coloring