Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables
Mathematics of Operations Research
Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Inferring Peptide Composition from Molecular Formulas
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Journal of Combinatorial Theory Series A
Making change and finding repfigits: balancing a knapsack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
The money changing problem revisited: computing the Frobenius number in time O(k a1)
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
A generalization of the integer linear infeasibility problem
Discrete Optimization
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We consider the following integer feasibility problem: "Given positive integer numbers a0, a1,..., an, with gcd(a1,..., an) = 1 and a = (a1,..., an), does there exist a nonnegative integer vector x satisfying ax = a0?" Some instances of this type have been found to be extremely hard to solve by standard methods such as branch-and-bound, even if the number of variables is as small as ten. We observe that not only the sizes of the numbers a0, a1,..., an, but also their structure, have a large impact on the difficulty of the instances. Moreover, we demonstrate that the characteristics that make the instances so difficult to solve by branch-and-bound make the solution of a certain reformulation of the problem almost trivial. We accompany our results by a small computational study.