Abstract
Graph colouring problem is a well-known NP-class optimization problem, studied due to a lot of applications in various real-world problems. Some of these applications are: register allocation, image processing and communication networks. There are various techniques suggested by the researchers to solve the problem which is either exact or approximate in nature. In this paper, a new greedy technique, based on degrees of vertices in the graph is presented to solve the graph colouring problem in an improved manner. The technique involves the use of adjacency matrix along with another matrix generated for the set of possible colours for each vertex in the graph. The generated colour matrix is used to assign the colours among the vertices in the graph based on decreasing degrees of the vertices. Several DIMACS colouring instances solved using the suggested approach in the article and compared with some contemporary techniques for the performance and proves compatible and having better execution time with compared technique. The obtained colouing results are mostly optimal colour values corresponding to the examined colouring instances of the graph.
Highlights
In recent years graph colouring problem is one of the most recurrent problems studied in the literature due to its capability to address a lot of application problems in the area of Engineering, communication networks and in other real-world problems
The graph colouring problem involves the mapping of the available distinct colours among the nodes in the graph so that neighbouring nodes must be allocated with distinct colours
In the proposed research work, we present a greedy technique for colouring of the vertices based on the computation of the degree of each vertex in the graph and using computed information and applying the colouring procedure to allocate the colour to each vertex in the graph
Summary
The researchers suggested an improved solution for the allocation of the registers by encoding the problem into colouring problem of graph Another application of the graph colouring problem is found in the time table scheduling. With the use of the genetic algorithm, researchers proposed an efficient solution to this problem by encoding it into graph colouring for successful mapping of the courses into the time table [3]. Another use of graph colouring problem comes from its use in address sorting in mailing process. The colouring scheme of vertices in the graph is based on the construction of a set of vertices in the decreasing order of degree and entire procedures implemented using array data structure to handle sets generated and matrices used to store graphs and other information
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