|Title||Variation of Cost Functions in Integer Programming|
|Author(s)|| Bernd Sturmfels, Rekha R. Thomas|
|Type||Article in Journal|
|Abstract||We study the problem of minimizing c cdot x subject to A cdot x = b,|
x ge 0 and x integral, for a fixed matrix A. Two cost functions c and c'
are considered equivalent if they give the same optimal solutions for each b. We construct a polytope St(A) whose normal cones are the equivalence classes. Explicit inequality presentations of these cones
are given by the reduced Grobner bases associated with A. The union of the reduced Grobner bases as c varies (called the universal Grobner basis) consists precisely of the edge directions of St(A). We present geometric algorithms for computing St(A), the Graver basis [Gra], and the
universal Grobner basis.