The Single Source Shortest Path (SSSP) problem consists in finding the shortest paths from a vertex (the source vertex) to all other vertices in a graph. SSSP has numerous applications. For some algorithms and applications, it is useful to solve the SSSP problem in parallel. This is the case of Betweenness Centrality which solves the SSSP problem for multiple source vertices in large graphs. In this paper, we introduce the Dijkstra Strip Mined Relaxation (DSMR) algorithm, an efficient parallel SSSP algorithm for shared and distributed-memory systems. We also introduce a set of preprocessing optimization techniques that significantly reduce the communication overhead without increasing the total amount of work dramatically. Our results show that, DSMR is faster than the best previous algorithm, parallel Δ-Stepping, by up-to 7.38×.