Convex hulls of superincreasing knapsacks and lexicographic orderings

Citations of this article
Mendeley users who have this article in their library.


We consider bounded integer knapsacks where the weights and variable upper bounds together form a superincreasing sequence. The elements of this superincreasing knapsack are exactly those vectors that are lexicographically smaller than the greedy solution to optimizing over this knapsack. We describe the convex hull of this n-dimensional set with O(n) facets. We also establish a distributive property by proving that the convex hull of ≤- and ≥-type superincreasing knapsacks can be obtained by intersecting the convex hulls of ≤- and ≥-sets taken individually. Our proofs generalize existing results for the 0\1 case.




Gupte, A. (2016). Convex hulls of superincreasing knapsacks and lexicographic orderings. Discrete Applied Mathematics, 201, 150–163.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free