Convex hulls of superincreasing knapsacks and lexicographic orderings

Akshay Gupte
2016 Discrete Applied Mathematics  
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
more » ... tersecting the convex hulls of <- and >-sets taken individually. Our proofs generalize existing results for the binary case.
doi:10.1016/j.dam.2015.08.010 fatcat:lzpvcljrc5bjfgy7pn7fjzbwjm