In Graph theory, Single Source Shortest Paths (SSSP) is one of the problems which can be easily solved sequentially using Dijkstra’s Algorithm, but it gets notoriously difficult in a parallel setting. This can be attributed to its transitive dependencies.In this thesis, we present our ideas on efficiently calculating shortest paths for road networks on shared memory architecture. We first discuss the performance of SSSP algorithms on random graphs and actual road networks. Then we present our improvements on shared memory implementation of Delta Stepping algorithm. By far, this is the only work-efficient algorithm that can solve SSSP in parallel. We discuss the performance of our Improved Delta Stepping algorithm on graphs of U.S. states road networks. In the end, we report comparisons between existing algorithm and its proposed variant.
