Adaptive and Cost-Optimal Parallel Algorithm for the 0-1 Knapsack Problem

Abstract

The 0-1 knapsack problem is well known to be NP-complete problem. In the past two decades, much effort has been done in order to find techniques that could lead to algorithms with a reasonable running time. This paper proposes a new parallel algorithm for the 0-1 knapsack problem where the optimal merging algorithm is adopted. Based on an EREW PRAM machine with shared memory, the proposed algorithm utilizes O((2^(n/4))^(1-e)) processors, 0 \le ε \le 1, and O(2^(n/2)) memory to find a solution for the n-element 0-1 knapsack problem in time O((2^(n/4))(2^(n/4))^e). Thus the cost of the proposed parallel algorithm is O(2^(n/2)), which is both the lowest upper-bound time and without memory conflicts if only quantity of objects is considered in the complexity analysis for the 0-1 knapsack problem. Thus it is an improvement result over the past researches.