An SIMD parallel ϵ-approximation scheme for 0/1 knapsack

A parallel version of a well-known ε-approximation scheme for 0/1 knapsack problems is presented. The model of computation for the parallelization is a shared memory machine in which processors have exclusive read, exclusive write access to memory. The scheme separates the knapsack items into two sets, one of which is used in a dynamic programming-based optimization procedure, and the other of which is used in a greedy selection process. A dominance relation exists for the knapsack problem which is used to limit the growth of feasible solutions during the dynamic programming procedure. The dominance relation permits a simple representation of the feasible solutions which aids in the parallelization of the dynamic programming procedure across all feasible solutions in parallel during the process of considering a new item. The algorithm uses max(n.32/ε³-8/ε) processors and takes O(n) time. For moderate values of ε and values of n which are quite large (tens of thousands of items), the algorithm is realizable on currently available, massively parallel computer systems, such as the Connection Machine system