In-place Recursive Approach for All-pairs Shortest Paths Problem Using Opencl

The all-pairs shortest paths (APSP) problem finds the shortest path distances between all pairs of vertices,and is one of the most fundamental graph problems. In this paper, a parallel recursive partitioning approach to APSP problem using Open Computing Language (OpenCL) for directed and dense graphs with no negative cyclesbased on R-Kleene algorithm, is presented, which recursively partitions dense adjacency matrix into sub-matrices and computes the shortest path. Graphics Processing Units (GPUs) are massively parallel in nature and provide high computational speedup at very low cost in comparison to other very costly High Performance Computing (HPC) systems. Most common technique for Graph representation is to store it in the form of adjacency matrix and GPUs are highly suitable for performing matrix computations in parallel. OpenCL is a framework which provides unified development environment for executing programs in heterogeneous platforms. Using OpenCL, we can execute program on GPUs and/or CPUs. Our implementation is mainly targeted towards executing OpenCL kernels on GPU. In designing effective OpenCL programs, data transfers between host and device memory should be minimized. Our approach is in-place in nature, so it does not require additional memory space while performing computation and entire data movement takes place in a bulk between host and device memory.