A Parallelization of Non-Serial Polyadic Dynamic Programming on GPU

Abstract

Parallelization of Non-Serial Polyadic Dynamic Programming (NPDP) on high-throughput manycore architectures, such as NVIDIA GPUs, suffers from load imbalance, i.e. non-optimal mapping between the sub-problems of NPDP and the processing elements of the GPU. NPDP exhibits non-uniformity in the number of subproblems as well as computational complexity across the phases. In NPDP parallelization, phases are computed sequentially whereas subproblems of each phase are computed concurrently. Therefore, it is essential to effectively map the subproblems of each phase to the processing elements while implementing thread level parallelism. We propose an adaptive Generalized Mapping Method (GMM) for NPDP parallelization that utilizes the GPU for efficient mapping of subproblems onto processing threads in each phase. Input-size and targeted GPU decide the computing power and the best mapping for each phase in NPDP parallelization. The performance of GMM is compared with different conventional parallelization approaches. For sufficiently large inputs, our technique outperforms the state-of-the-art conventional parallelization approach and achieves a significant speedup of a factor 30. We also summarize the general heuristics for achieving better gain in the NPDP parallelization.

Coarse-grained multicomputer parallel algorithm using the four-splitting technique for the minimum cost parenthesizing problem

“…Shyamala et al [11] accelerated the computation time through C++ high-performance accelerated massive parallel code. More recently, Diwan and Tembhurne [13] designed an adaptive generalized mapping method to parallelize non-serial polyadic dynamic-programming problems that utilize GPUs, for efficient mapping of subproblems onto processing threads in each phase. Biswas and Mukherjee [14] proposed a new memory optimized technique and a versatile technique of utilizing shared memory in blocks of threads to minimize time for accessing dimensions of matrices on GPU architectures.…”

A fast sequential algorithm for the matrix chain ordering problem

“…Shyamala et al 23 accelerated the computation time through C++ high-performance accelerated massive parallel code. More recently, Diwan and Tembhurne 24 designed an adaptive generalized mapping method to parallelize polyadic-nonserial dynamic-programming problems that utilize GPUs, for efficient mapping of subproblems onto processing threads in each phase. On shared-memory architectures, Tan et al 25 proposed a parallel algorithm based on a pipeline to fill the dynamic-programming table by decomposing the calculation operators.…”

“…{512,1024, 2048, 4096, 8192,12,288,16,384,20,480,24,576,28,672, 32,768, 36,864, 40,960, 45,056, 49,152, 53,248, 57,344, 61,440, 65,536}, and p is the number of processors, with values in the set ‡ https://www.u-picardie.fr/recherche/presentation/plateformes/plateforme-matrics-382844.kjsp {1, 8, 16, 32}. We compare our dynamic-programming solution with Yao's sequential algorithm and our previous solution (seeSection 4.3).…”