A GPU Parallel Approximation Algorithm for Scheduling Parallel Identical Machines to Minimize Makespan

We present a parallel approximation algorithm for the problem of scheduling jobs on parallel identical machines to minimize makespan which is designed and optimized for running efficiently on the GPU. The algorithm is a Polynomial Time Approximation Scheme (PTAS) based on a higher-dimensional dynamic programming approach, where dimensionality refers to the number of variables in the dynamic programming equation characterizing the problem. The main component of our design consists of a novel data-partitioning technique that is employed to accelerate the higher-dimensional dynamic programming component of the algorithm. We present performance results to demonstrate how our proposed design improves the GPU utilization and makes it possible to solve large higher-dimensional dynamic programming problems with the limited GPU memory. Experimental results show that the GPU implementation outperforms the optimized OpenMP implementation of the approximation algorithm.