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In this paper, we will show that the width of simplices defined by systems oflinear inequalities can be computed in polynomial time if some minors of theirconstraint matrices are bounded. Additionally, we present somequasi-polynomial-time and polynomial-time algorithms to solve the integerlinear optimization problem defined on simplices minus all their integervertices assuming that some minors of the constraint matrices of the simplicesare bounded.

The Width and Integer Optimization on Simplices With Bounded Minors of the Constraint Matrices