# Computing holes in semi-groups and its applications to transportation problems

@article{Hemmecke2006ComputingHI, title={Computing holes in semi-groups and its applications to transportation problems}, author={Raymond Hemmecke and Akimichi Takemura and Ruriko Yoshida}, journal={Contributions to Discrete Mathematics}, year={2006}, volume={4} }

An integer feasibility problem is a fundamental problem in many areas,
such as operations research, number theory, and statistics.
To study a family of systems with no nonnegative integer solution, we focus
on a commutative semigroup generated by a finite
set of vectors in $\Z^d$ and its saturation. In this paper
we present an algorithm to compute an explicit description for the
set of holes which is the difference of a semi-group $Q$ generated
by the vectors and its saturation… CONTINUE READING

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