A near linear shortest path algorithm for weighted undirected graphs

This paper presents an algorithm for Shortest Path Tree (SPT) problem. The presented algorithm is an improvement over a previously published work of the authors. The effort is put in to improve the running/execution time of the SPT problem. Introduced improvement is simple and easy to incorporate in to the existing algorithm. This algorithm uses Depth First Search (DFS) like graph traversal during a BFS like traversal i.e. combines and take advantage of the inherent properties of the two heuristic graph search techniques so that vertex weights can be kept balanced. The need of improvement is discussed in detail and the expected improvement in overall processing time is shown with the example.