Details:
Title  A geometric Buchberger algorithm for integer programming  Author(s)  Rekha R. Thomas  Type  Article in Journal  Abstract  Let IP denote the family of integer programs of the form Min cx : Ax
= b, x in N^n obtained by varying the right hand side vector b but keeping A and c fixed. A test set for IP is a set of vectors in Z^n such that for each nonoptimal solution ff to a program in this family, there is at least one element g in this set such that alpha  g has an improved cost value as compared to alpha. We describe a unique minimal test set for this family called the reduced Grobner basis of IP. An algorithm for its construction is presented which we call a Geometric Buchberger Algorithm for integer programming. We show how an integer program may be solved using this test set and examine some geometric properties of elements in the set. The reduced Grobner basis is then compared with some other known test sets from the literature. We also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix A in Z^{(n  2) times n} of full row rank.  Keywords  integer programming, test sets, reduced Gröbner basis, Buchberger algorithm, fiber, Hilbert bases 
Language  English  Journal  Mathematics of Operations Research  Volume  20  Pages  864884  Year  1995  Month  September  Translation 
No  Refereed 
No 
