Computation of Atomic Fibers of Z-Linear Maps
Raymond Hemmecke
Abstract
For given matrix A∈d× n, the set PIA,b=\z:Az=b,z∈n+\ describes the preimage or fiber of b∈d under the -linear map fA:n+d, x Ax. The fiber PIA,b is called atomic, if PIA,b=PIA,b1+PIA,b2 implies b=b1 or b=b2. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, application to integer programming, and computational examples are included as well.
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