/ On Facets of Knapsack Equality Polytopes

نویسنده

  • E. K. Lee
چکیده

The 0/1 knapsack equality polytope is, by deenition, the convex hull of 0/1 solutions of a single linear equation. A special form of this polytope | where the deening linear equation has nonnegative integer coeecients and the number of variables having co-eecient one exceeds the right-hand-side | is considered. Equality constraints of this form arose in a real-world application of integer programming to a truck dispatching scheduling problem. Families of facet deening inequalities for this polytope are identiied, and complete linear inequality representations are obtained for some classes of polytopes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Some Results on facets for linear inequality in 0-1 variables

The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...

متن کامل

Equality Set Projection: A new algorithm for the projection of polytopes in halfspace representation

In this paper we introduce a new algorithm called Equality Set Projection (ESP) for computing the orthogonal projection of bounded, convex polytopes. Our solution addresses the case where the input polytope is represented as the intersection of a finite number of halfplanes and its projection is given in an irredundant halfspace form. Unlike many existing approaches, the key advantage offered b...

متن کامل

An 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 کامل

Revlex-initial 0/1-polytopes

We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are special knapsack-polytopes. It turns out that they have remarkable extremal properties. In particular, we use these polytopes in order to prove that the minimum numbers gnfac(d, n) of facets and the minimum average degree gavdeg(d, n) of the graph of a d...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997