Optimal parallel algorithm for the knapsack problem without memory conflicts

Abstract

The knapsack problem is very important in cryptosystem and in number theory. We propose a new parallel algorithm for the knapsack problem where the method of divide and conquer is adopted. Basing on an EREW-SIMD machine with shared memory, the proposed algorithm utilizes O(2/sup n/4/)/sup 1-/spl epsiv// processors, 0/spl les//spl epsiv//spl les/1, and O(2/sup n/) memory to find a solution for the n-element knapsack problem in time O(2/sup n/4/ (2/sup n/4/)/sup /spl epsiv//). Thus the cost of the proposed parallel algorithm is O(2/sup n/), which is optimal, and an improved result over the past researches.