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09/11/2022
Structured (min,+)-Convolution And Its Applications For The Shortest Vector, Closest Vector, and Separable Nonlinear Knapsack Problems
In this work we consider the problem of computing the (min, +)-convoluti...
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03/08/2022
On a Simple Connection Between Δ-modular ILP and LP, and a New Bound on the Number of Integer Vertices
Let A ∈ Z^m × n, rank(A) = n, b ∈ Z^m, and P be an n-dimensional polyhed...
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10/04/2021
Faster algorithm for counting of the integer points number in Δ-modular polyhedra
Let a polytope 𝒫 be defined by one of the following ways: (i) 𝒫 = {x ∈...
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03/12/2021
An FPTAS for the Δ-modular multidimensional knapsack problem
It is known that there is no EPTAS for the m-dimensional knapsack proble...
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11/01/2020
A polynomial algorithm for minimizing discrete convic functions in fixed dimension
Recently classes of conic and discrete conic functions were introduced. ...
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10/12/2020
On lattice point counting in Δ-modular polyhedra
Let a polyhedron P be defined by one of the following ways: (i) P = {x...
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02/03/2020
A note on the parametric integer programming in the average case: sparsity, proximity, and FPT-algorithms
We consider the Integer Linear Programming (ILP) problem max{c^ x : A x ...
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02/03/2020
Properties of Δ-modular simplicies and "close" polyhedrons. O(Δ· polylog(Δ))-algorithm for knapsack, proximity and sparsity
In this work we consider properties of square and "close"-square Δ-modul...
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07/08/2018
On the complexity of quasiconvex integer minimization problem
In this paper, we consider the class of quasiconvex functions and its pr...
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12/18/2017
FPT-algorithms for some problems related to integer programming
In this paper, we present FPT-algorithms for special cases of the shorte...
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10/01/2017
The Width and Integer Optimization on Simplices With Bounded Minors of the Constraint Matrices
In this paper, we will show that the width of simplices defined by syste...
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10/01/2017
