Computation of Atomic Fibers of Z-Linear Maps

For given matrix $A\in\Z^{d\times n}$, the set $P_{b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P_{b}$ is called atomic, if $P_{b}=P_{b_1}+P_{b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, computational examples and applications are included as well.Comment: 27 page

Computation of atomic fibers of Z-linear maps

For given matrix $A\in\Z^{d\times n}$, the set $P_{b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\rightarrow\Z^d$, $x\mapsto Ax$. The fiber $P_{b}$ is called atomic, if $P_{b}=P_{b_1}+P_{b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, computational examples and applications are included as well

Finiteness theorems in stochastic integer programming

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many ``building blocks'', independent of the number of scenarios, and we give an effective procedure to compute these building blocks. The paper includes an introduction to Nash-Williams' theory of better-quasi-orderings, which is used to show termination of our algorithm. We also apply this theory to finiteness results for Hilbert functions.Comment: 36 p

Computation of atomic fibers of Z-linear maps

For given matrix $A\in\Z^{d\times n}$, the set $P_{b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\rightarrow\Z^d$, $x\mapsto Ax$. The fiber $P_{b}$ is called atomic, if $P_{b}=P_{b_1}+P_{b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, computational examples and applications are included as well

Computation of Atomic Fibers of Z-Linear Maps

For given matrix $A\in\Z^{d\times n}$, the set $P_{b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P_{b}$ is called atomic, if $P_{b}=P_{b_1}+P_{b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, computational examples and applications are included as well