Dmitry V. Gribanov

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In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their(More)
Let A be an (m × n) integral matrix, and let P = {x : Ax ≤ b} be an n-dimensional polytope. The width of P is defined as w(P ) = min{x ∈ Z\{0} : maxx∈Pxu−minx∈Pxv}. Let ∆(A) and δ(A) denote the greatest and the smallest absolute values of a determinant among all r(A)× r(A) submatrices of A, where r(A) is the rank of a matrix A. We prove that if every r(A) ×(More)
Let A be an m × n integral matrix of rank n. We say that A has bounded minors if the maximum of the absolute values of the n × n minors is at most k, where k is a some natural constant. We will call that matrices like k-modular. We investigate an integer program max{cx : Ax ≤ b, x ∈ Zn} where A is k-modular. We say that A is almost unimodular (see [2, 5])(More)
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