Adjacency of the 0-1 knapsack problem

In this paper the authors 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 knpasack problem, there u and v are nonadjacent on the polytope of the convex hull of feasible solutions, if and only if, there exist two other feasible solutins w¹ and w², such hat 1/2w¹+1/2w²=1/u+1/2v. This observation allows the authors to prove that the question of determining whether two given feasible solutions are adjacent, is an NP-complete problem.