Dense Dynamic Programming on Multi GPU

Abstract

Abstract-The implementation via CUDA of a hybrid dense dynamic programming method for knapsack problems on a multi-GPU architecture is considered. Tests are carried out on a Bull cluster with Tesla S1070 computing systems. A first series of computational results shows substantial speedup close to 30 with two GPUs.

Recent Advances on GPU Computing in Operations Research

“…The solution of KP via a hybrid dense dynamic programming algorithm implemented with CUDA 2.0 has been considered in [22]. At each step, computations in the loop that processes the classical Bellman's dynamic programming recursion (which is time consuming) have been implemented in parallel on the device.…”

“…The contribution in [22] has been further extended in [23], where a multi-GPU hybrid implementation via CUDA 2.3 of the dense dynamic programming method has been proposed. The approach is well suited to the case where a CPU is connected to several GPUs.…”

Parallelization and checkpointing of GPU applications through program transformation

“…In the domain of manual instrumentation, several works present multi-GPU implementations of dense algebra operations [33], linear programming [34], optimization problems [35], computational fluid dynamics [36], medical imaging [37,38], signal processing [39], among others. All these works apply techniques for achieving fine tuned implementations of their problems.…”

Efficient Implementation of the Simplex Method on a CPU-GPU System

“…GPUs are highly parallel, multithreaded, manycore units. In November 2006, NVIDIA introduced, Compute Unified Device Architecture (CUDA), a technology that enables users to solve many complex problems on their GPU cards (see for example [1] - [4]). Some related works have been presented on the parallel implementation of algorithms on GPU for linear programming (LP) problems.…”

“…For example, one has to solve frequently linear programming problems for bound computation purpose when one uses branch and bound algorithms and it may happen that some instances give rise to dense LP problems. The present work is part of a study on the parallelization of optimization methods (see also [1]). The paper is structured as follows.…”