TY - GEN A1 - Thomas, Rekha R. A1 - Weismantel, Robert T1 - Test sets and inequalities for integer programs: extended abstract N2 - This paper presents some connections between test sets and valid inequalities of integer programs. The reason for establishing such relationships is the hope that information (even partial) on one of these objects can be used to get information on the other and vice versa. We approach this study from two directions: On the one hand we examine the geometric process by which the secondary polytope associated with a matrix $A$ transforms to the state polytope as we pass from linear programs that have $A$ as coefficient matrix to the associated integer programs. The second direction establishes the notion of classes of augmentation vectors parallel to the well known concept of classes of facet defining inequalities for integer programs. We show how certain inequalities for integer programs can be derived from test sets for these programs. T3 - ZIB-Report - SC-95-36 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2021 ER - TY - GEN A1 - Thomas, Rekha R. A1 - Weismantel, Robert T1 - Truncated Gröbner Bases for Integer Programming N2 - {\def\N{{\mbox{{\rm I\kern-0.22emN}}}}In this paper we introduce a multivariate grading of the toric ideal associated with the integer program $min \{ cx : Ax = b, x \in \N^n \}$, and a truncated Buchberger algorithm to solve the program. In the case of $max \{ cx : Ax \leq b, x \leq u, x \in \N^n \}$ in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in UWZ94}. T3 - ZIB-Report - SC-95-09 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1750 ER -