Solving path problems on the GPU

Abstract

We consider the computation of shortest paths on Graphic Processing Units (GPUs). The blocked recursive elimination strategy we use is applicable to a class of algorithms (such as all-pairs shortest-paths, transitive closure, and LU decomposition without pivoting) having similar data access patterns. Using the all-pairs shortest-paths problem as an example, we uncover potential gains over this class of algorithms. The impressive computational power and memory bandwidth of the GPU make it an attractive platform to run such computationally intensive algorithms. Although improvements over CPU implementations have previously been achieved for those algorithms in terms of raw speed, the utilization of the underlying computational resources was quite low. We implemented a recursively partioned all-pairs shortest-paths algorithm that harnesses the power of GPUs better than existing implementations. The alternate schedule of path computations allowed us to cast almost all operations into matrix-matrix multiplications on a semiring. Since matrix-matrix multiplication is highly optimized and has a high ratio of computation to communication, our implementation does not suffer from the premature saturation of bandwidth resources as iterative algorithms do. By increasing temporal locality, our implementation runs more than two orders of magnitude faster on an NVIDIA 8800 GPU than on an Opteron. Our work provides evidence that programmers should rethink algorithms instead of directly porting them to GPU.

Applications of Ear Decomposition to Efficient Heterogeneous Algorithms for Shortest Path/Cycle Problems

“…[9]) has been the choice of several parallel implementation as the algorithm allows one to study cache blocking techniques. Examples of this approach can be seen in Buluc et al [5], Matsumoto et al [28] and Katz et al [23]. The above works report results on a variety of CPU and GPU architectures.…”

“…As graphs corresponding to real-world and practical applications have a massive size, parallel processing is often necessary. It is therefore natural that a lot of current research is directed towards efficient algorithmics on a variety of modern and emerging multi-and many-core architectures [4,28,5,34].…”

Minimizing Communication in All-Pairs Shortest Paths

“…Actual algorithms based on this proof are given by various researchers, with minor differences. Our decision to use the DC algorithm as our starting point is inspired by its demonstrated better cache reuse on CPUs [33], and its impressive performance attained on the many-core graphical processor units [11].…”

“…SSSP algorithms based on ∆-stepping [32] scale better in practice but their performance is input dependent and scales with O(m+d·L·log n), where d is the maximum vertex degree and L is the maximum shortest path weight from the source. Consequently, it is likely that a Floyd-Warshall based approach would be competitive even for sparse graphs, as realized on graphical processing units [11].…”

Acceleration of Computing the Kleene Star in Max-Plus Algebra Using CUDA GPUs

“…In particular, recent GPU cards produced by NVIDIA Corporation provide substantial benefits for parallel computation, and the company itself supplies an easyto-implement environment for developers and researchers. Recently, the effectiveness and advantages of using GPUs for technical computations have been widely reported [6]- [8].…”