An O(n log n) procedure for identifying facets of the knapsack polytope
نویسندگان
چکیده
An O(n log n) procedure is presented for obtaining facets of the knapsack polytope by lifting the inequalities induced by the extensions of strong minimal covers. The procedure does not require any sequential lifting of the inequalities. In contrast, it utilizes the information from the maximal cliques implied by the knapsack constraint for determining the combination of the lifting coe4cients to generate each facet. c © 2003 Elsevier Science B.V. All rights reserved.
منابع مشابه
The Complexity of Lifted Inequalities for the Knapsack Problem
Hartvigsen, D. and E. Zemel, The complexity of lifted inequalities for the knapsack problem, Discrete Applied Mathematics 39 (1992) 11. 123. It is well known that one can obtain facets and valid inequalities for the knapsack polytope by lifting simple inequalities associated with minimal covers. We study the complexity of lifting. We show that recognizing integral lifted facets or valid inequal...
متن کاملConstruction de facettes pour le polytope du sac-à-dos quadratique en 0-1
We build facets of the quadratic 0-1 knapsack polytope following two different approaches. The quadratic 0-1 knapsack polytope is included in the Boolean quadric polytope introduced by Padberg [12] for unconstrained 0-1 quadratic problem. So in a first approach, we ask the question which are the facets of the Boolean quadric polytope that are still facets of the quadratic 0-1 knapsack polytope....
متن کاملHilbert Bases and the Facets of Special Knapsack Polytopes
Let a set N of items, a capacity F 2 IN and weights a i 2 IN, i 2 N be given. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality X i2N a i x i F: In this paper we present a linear description of the 0/1 knapsack polytope for the special case where a i 2 f; g for all items i 2 N and 1 < b are two natural numbers. The inequalities needed for this descripti...
متن کاملAn FPTAS for the Volume of Some V -polytopes - It is Hard to Compute the Volume of the Intersection of Two Cross-Polytopes
Given an n-dimensional convex body by a membership oracle in general, it is known that any polynomial-time deterministic algorithm cannot approximate its volume within ratio (n/ logn). There is a substantial progress on randomized approximation such as Markov chain Monte Carlo for a highdimensional volume, and for many #P-hard problems, while some deterministic approximation algorithms are rece...
متن کامل0/1 Polytopes with Quadratic Chvátal Rank
For a polytope P , the Chvátal closure P ′ ⊆ P is obtained by simultaneously strengthening all feasible inequalities cx ≤ β (with integral c) to cx ≤ ⌊β⌋. The number of iterations of this procedure that are needed until the integral hull of P is reached is called the Chvátal rank. If P ⊆ [0, 1], then it is known that O(n log n) iterations always suffice (Eisenbrand and Schulz (1999)) and at lea...
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