| Article ID: | iaor1988269 |
| Country: | Germany |
| Volume: | 19 |
| Start Page Number: | 889 |
| End Page Number: | 894 |
| Publication Date: | Oct 1988 |
| Journal: | Optimization |
| Authors: | Hujter M. |
| Keywords: | knapsack problem |
Some known results about lower and upper bounds for the number of distinct solutions to a discrete knapsack problem are given. In this paper some sharper bounds are proved by using geometrical methods. The proof of the upper bound is based on the famous (and deep) Brunn-Minkowski inequality, and it is a new and interesting application method of geometrical arguments in discrete programming.