A survey of parallel algorithms for one-dimensional integer knapsack problems

This article surveys several methods that can be used to solve integer knapsack problems on a variety of parallel computing architectures. Parallel algorithms designed for a variety of one-dimensional knapsack problems on both theoretical PRAM models of computation and existing parallel architectures are examined. First, exact parallel algorithms for one-dimensional exact sum, unbounded, and 0/1 knapsack problems are reviewed. These algorithms were developed from sequential table-based approaches, dynamic programming formulations, and reduction to circuit-valued or prefix convolution problems. Next, greedy algorithms and approximation algorithms for the one-dimensional subset sum, subset product, and 0/1 knapsack problems are also discussed. Experimental results that have been reported in the literature are summarized throughout this report.