Theory of linear and integer programming
Theory of linear and integer programming
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Hard Equality Constrained Integer Knapsacks
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Buchberger Algorithm and Integer Programming
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Non-standard approaches to integer programming
Discrete Applied Mathematics
The Mathematica Book
Circulant digraphs and monomial ideals
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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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.