GRIN: An implementation of Gröbner bases for integer programming. this paper we present a computer program (GRIN) for solving and analyzinginteger programs using Grobner bases. The algorithms coded in GRIN aredrawn from both commutative algebra and the standard IP repertoire (e.g. Lovasz’reduced lattice bases). We present two new algorithms for computing generatorsof toric ideals. One of them is due to DiBiase and Urbanke. The emphasis ofour discussion lies on experiments and practical computability...

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  1. Charalambous, Hara; Thoma, Apostolos; Vladoiu, Marius: Minimal generating sets of lattice ideals (2017)
  2. Charalambous, Hara; Thoma, Apostolos; Vladoiu, Marius: Binomial fibers and indispensable binomials (2016)
  3. Braun, Volker: The 24-cell and Calabi-Yau threefolds with Hodge numbers $(1,1)$ (2012)
  4. Haus, Utz-Uwe; Hemmecke, Raymond; Pokutta, Sebastian: Reconstructing biochemical cluster networks (2011)
  5. Kahle, Thomas: Decompositions of binomial ideals (2010)
  6. Kesh, Deepanjan; Mehta, Shashank K.: Generalized reduction to compute toric ideals (2010)
  7. Blanco, Víctor; Puerto, Justo: Partial Gröbner bases for multiobjective integer linear optimization (2009)
  8. Hemmecke, Raymond; Malkin, Peter N.: Computing generating sets of lattice ideals and Markov bases of lattices (2009)
  9. Carrà Ferro, Giuseppa; Ferrarello, Daniela: Ideals and graphs, Gröbner bases and decision procedures in graphs (2008)
  10. Bogart, Tristram; Jensen, Anders N.; Thomas, Rekha R.: The circuit ideal of a vector configuration (2007)
  11. Craw, Alastair; Maclagan, Diane; Thomas, Rekha R.: Moduli of McKay quiver representations. II: Gröbner basis techniques (2007)
  12. Craw, Alastair; Maclagan, Diane; Thomas, Rekha R.: Moduli of McKay quiver representations. I: The coherent component (2007)
  13. Briales-Morales, Emilio; Campillo-López, Antonio; Pisón-Casares, Pilar; Vigneron-Tenorio, Alberto: Minimal resolutions of lattice ideals and integer linear programming (2003)
  14. Crema, Alejandro: The multiparametric 0-1-integer linear programming problem: A unified approach (2002)
  15. Briales-Morales, E.; Pisón-Casares, P.; Vigneron-Tenorio, A.: The regularity of a toric variety (2001)
  16. Pisón-Casares, P.; Vigneron-Tenorio, A.: First syzygies of toric varieties and Diophantine equations in congruence (2001)
  17. Hoşten, Serkan; Shapiro, Jay: Primary decomposition of lattice basis ideals (2000)
  18. Schultz, Rüdiger; Stougie, Leen; van der Vlerk, Maarten H.: Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reductions (1998)
  19. Weismantel, Robert: Test sets of integer programs (1998)
  20. Li, Qiang; Guo, Yi-ke; Ida, Tetsuo; Darlington, John: The minimised geometric Buchberger algorithm: An optimal algebraic algorithm for integer programming (1997)

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