A hypercube algorithm for the 0/1 Knapsack problem

Abstract

Many combinatorial optimization problems are known to be NP-complete. A common point of view is that finding fast algorithms for such problems using polynomial number of processors is unlikely. However, facts of this kind usually are established for “worst” case situations and in practice many instances of NP-complete problems are successfully solved in polynomial time by such traditional combinatorial optimization techniques as dynamic programming and branch-and-bound. New opportunities for effective solution of combinatorial problems emerged with the advent of parallel machines. In this paper we describe an algorithm which generates an optimal solution for the 0/1 integer Knapsack problem on the NCUBE hypercube computer. It is also demonstrated that the same algorithm can be applied for the two-dimensional 0/1 Knapsack problem. Experimental data which support the theoretical claims are provided for large instances of the one- and two-dimensional Knapsack problems.