ADJACENCY OF THE 0-1 KNAPSACK-PROBLEM

In this paper we show that adjacency on the 0-1 knapsack polytope can be determined by a very simple argument. Namely, let u and v be two feasible solutions to the 0-1 knapsack problem, then u and v, are nonadjacent on the polytope of the convex hull of feasible solutions, if and only if, there exist two other feasible solutions w1 and w2, such that 1/2w1 + 1/2w2 = 1/u + 1/2v. This observation allows us to prove that the question of determining whether two given feasible solutions are adjacent, is an NP-complete problem.