An Experimental Analysis of Vertex Coloring Algorithms on Sparse Random Graphs

The DSATUR algorithm for vertex coloring is popular both in its heuristic and exact (branch-and-bound) forms. Common to the known public implementations of the exact algorithm is the use of adjacency matrices to store the adjacency relations; this influences the algorithm's implementation and its running time. In this paper we investigate the benefits of the introduction of supporting data structures to improve its running time: in addition to replacing the adjacency matrix by adjacency lists, thus shifting the focus from vertices to edges, we also introduce a priority queue data structure to assist in vertex selection. Our goal is to explore under which circumstances additional supporting data structures can speed up (exact) DSATUR.