Implementation of K-shortest Path Algorithm in GPU Using CUDA

Abstract

K-shortest path algorithm is generalization of the shortest path algorithm. K-shortest path is used in various fields like sequence alignment problem in molecular bioinformatics, robot motion planning, path finding in gene network where speed to calculate paths plays a vital role. Parallel implementation is one of the best ways to fulfill the requirement of these applications. A GPU based parallel algorithm is developed to find k number of shortest path in a positive edge-weighted directed large graph. In calculated shortest path repetition of the vertices is not allowed. Implemented algorithm calculates a k-shortest path between two pair of vertices of a graph with n nodes and m vertices. This approach is based on Yen's algorithm to find k-shortest loopless path. We implemented our algorithms in Nvidia's GPU using Compute Unified Device Architecture (CUDA). This paper presents comparative analysis between CPU and GPU based implementation of Yen's Algorithm. Our approach achieves the 6 time speed up in comparison of serial algorithm.

Locality-Based Relaxation: An Efficient Method for GPU-Based Computation of Shortest Paths

“…As such, we would like to minimize the number of atomic statements. In addition to our algorithm and Harish et al's [12,13], Singh et al [26], Chaibou et al [6] and Ortega et al [20,21] present algorithms with just one atomic statement. Chaibou et al [6] evaluate the cost of memory copy between CPU and GPU.…”

“…We implement our algorithm in CUDA version 7.5. [16,25,26] with a speed up of at most 2.6 (see Table 2). We have run both algorithms on the same platform and same graphs.…”

“…Comparison with related work Observe that our algorithm and that of Singh et al[26] outperform the rest.…”

“…Most existing GPU-based algorithms [12,13,26,25,15,5] for solving SSSP rely on methods that associate a group of vertices/arcs to thread blocks, and optimize a proper subset of the aforementioned factors, but not all. This is because in general it is hard to determine the workload of each kernel for optimum efficiency a priori.…”

“…For example, Harish et al [12,13] present a GPU-based implementation of Dijkstra's shortest path algorithm [9] where they design two kernels; one for relaxing the recently updated vertices, called the frontier, and the second one for updating the list of frontier vertices. Singh et al [26] improve Harish et al's algorithm by using memory efficiently and using just one kernel. They also present a parallelization of Bellman-Ford's algorithm [3,11], but use three atomic operations in the kernel.…”