Integer and combinatorial optimization
Integer and combinatorial optimization
On an installation of Buchberger's algorithm
Journal of Symbolic Computation
Minimal solutions of linear diophantine systems: bounds and algorithms
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A geometric Buchberger algorithm for integer programming
Mathematics of Operations Research
Variation of cost functions in integer programming
Mathematical Programming: Series A and B
Journal of Symbolic Computation
GRIN: An Implementation of Gröbner Bases for Integer Programming
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Test Sets and Inequalities for Integer Programs
Proceedings of the 5th 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
Decomposition of Integer Programs and of Generating Sets
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Toric ideals of homogeneous phylogenetic models
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Generalized Reduction to Compute Toric Ideals
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Support sets in exponential families and oriented matroid theory
International Journal of Approximate Reasoning
A saturation algorithm for homogeneous binomial ideals
ACM Communications in Computer Algebra
A saturation algorithm for homogeneous binomial ideals
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Computing Gröbner bases of pure binomial ideals via submodules of Zn
Journal of Symbolic Computation
On decomposable semigroups and applications
Journal of Symbolic Computation
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In this article, we present an algorithm for computing generating sets of lattice ideals or equivalently for computing Markov bases of lattices. Generating sets of lattice ideals and Markov bases of lattices are essentially equivalent concepts. In contrast to other existing methods, the algorithm in this article computes with projections of lattices. This algorithm clearly outperforms other algorithms in our computational experience. Two areas of application for generating sets of lattice ideals and Markov bases lattices are algebraic statistics and integer programming.