Modified Dijkstra’s Algorithm for Dense Graphs on GPU using CUDA

Abstract

The objective of this research is to propose and implement a fast parallel Single source shortest path (SSSP) algorithm on Graphics Processing Unit (GPU) based highly parallel and cost effective platform for dense and complete graphs. The proposed algorithm is a variant of Dijkstra’s algorithm for SSSP calculation for complete and dense graphs. In place of relaxing all the edges of a selected node as in Dijkstra’s algorithm, it relaxes one-one selected edge of different nodes of the graph simultaneously at any iteration. This paper shows parallel implementation of both Dijkstra’s algorithm and our modified Dijkstra’s algorithm on a GPU-based machine. We evaluate these implementations on NVIDIA Tesla C2075 GPU- based machines. Parallel implementation of proposed modified Dijkstra’s algorithm gives a two to three times speed increase over a parallel Dijkstra’s algorithm on a GPU-based machine for complete and dense graphs. The proposed algorithm has minimized the number of edges relaxed by one parallel thread at any iteration of parallel Dijkstra’s algorithm.