Complete description of a class of knapsack polytopes
نویسندگان
چکیده
We study the knapsack polytopes that arise whenever the item weights are of two types: either of weight 1 or of weight p. A complete linear description of the associated integral polytope is given by showing that the system is TDI.
منابع مشابه
NP-Completeness of Non-Adjacency Relations on Some 0-1 Polytopes
In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.
متن کاملOn the 0/1 knapsack polytope
Given a set N of items and a capacity b 2 IN, and let N j be the set of items with weight j, 1 j b. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality b X j=1 X i2N j jx i b: In this paper we rst present a complete linear description of the 0/1 knapsack polytope for two special cases: (a) N j = ; for all 1 < j b b 2 c and (b) N j = ; for all 1 < j b b 3 ...
متن کاملOn the family of 0/1-polytopes with NP-complete non-adjacency relation
In 1995 T. Matsui considered a special family 0/1-polytopes for which the problem of recognizing the non-adjacency of two arbitrary vertices is NP-complete. In 2012 the author of this paper established that all the polytopes of this family are present as faces in the polytopes associated with the following NP-complete problems: the traveling salesman problem, the 3-satisfiability problem, the k...
متن کاملAn Efficient Algorithm for Reducing the Duality Gap in a Special Class of the Knapsack Problem
A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...
متن کاملAn Efficient Algorithm for Reducing the Duality Gap in a Special Class of the Knapsack Problem
A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Oper. Res. Lett.
دوره 31 شماره
صفحات -
تاریخ انتشار 2003