Gröbner Bases in Integer Programming

Rekha R. Thomas ()
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Rekha R. Thomas: Texas A&M University, Department of Mathematics

A chapter in Handbook of Combinatorial Optimization, 1998, pp 533-572 from Springer

Abstract: Abstract Recently, application of the theory of Gröbner bases to integer programming has given rise to new tools and results in this field. Here we present this algebraic theory as the natural integer analog of the simplex approach to linear programming Although couched in algebra, the theory of Gröbner bases and its consequences for integer programming are intimately intertwined with polyhedral geometry and lattice arithmetic which are staples of the traditional approach to this subject.

Keywords: Integer Program; Monomial Ideal; Cost Vector; Regular Triangulation; Graver Basis (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0303-9_8

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DOI: 10.1007/978-1-4613-0303-9_8

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