3 research outputs found
Recognition of Facets for Knapsack Polytope is DP-complete
DP is a complexity class that is the class of all languages that are the
intersection of a language in NP and a language in co-NP, as coined by
Papadimitriou and Yannakakis. In this paper, we will establish that,
recognizing a facet for the knapsack polytope is DP-complete, as conjectured by
Hartvigsen and Zemel in 1992. Moreover, we show that the recognition problem of
a supporting hyperplane for the knapsack polytope and the exact knapsack
problem are both DP-complete, and the membership problem of knapsack polytope
is NP-complete