Abstract
We will discuss knapsack problems that arise in certain computational number theory settings. A common theme is that the search space for the standard real relaxation is large; in a sense this translates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to computation of Frobenius instances, Keith numbers (also called “repfigits”), and as a first step in computation of Frobenius numbers.
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Lichtblau, D. (2006). Making Change and Finding Repfigits: Balancing a Knapsack. In: Iglesias, A., Takayama, N. (eds) Mathematical Software - ICMS 2006. ICMS 2006. Lecture Notes in Computer Science, vol 4151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832225_16
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DOI: https://doi.org/10.1007/11832225_16
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