An O(n) algorithm for the linear multiple choice knapsack problem and related problems
Information Processing Letters
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Sensitivity theorems in integer linear programming
Mathematical Programming: Series A and B
A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
The relationship between integer and real solutions of constrained convex programming
Mathematical Programming: Series A and B
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Dynamic programming revisited: improving knapsack algorithms
Computing - Special issue on combinatorial optimization
Linear time algorithms for knapsack problems with bounded weights
Journal of Algorithms
Cyclical scheduling and multi-shift scheduling: Complexity and approximation algorithms
Discrete Optimization
| Hi-index | 0.00 |
We consider the bounded integer knapsack problem (BKP) max@?"j"="1^np"jx"j, subject to: @?"j"="1^nw"jx"j@?C, and x"j@?{0,1,...,m"j},j=1,...,n. We use proximity results between the integer and the continuous versions to obtain an O(n^3W^2) algorithm for BKP, where W=max"j"="1","...","nw"j. The respective complexity of the unbounded case with m"j=~, for j=1,...,n, is O(n^2W^2). We use these results to obtain an improved strongly polynomial algorithm for the multicover problem with cyclical 1's and uniform right-hand side.