An algorithmic theory of integer programming

F Eisenbrand, C Hunkenschröder, KM Klein… - arxiv preprint arxiv …, 2019 - arxiv.org
We study the general integer programming problem where the number of variables $ n $ is a
variable part of the input. We consider two natural parameters of the constraint matrix $ A …

Block-structured integer and linear programming in strongly polynomial and near linear time

J Cslovjecsek, F Eisenbrand, C Hunkenschröder… - Proceedings of the 2021 …, 2021 - SIAM
We consider integer and linear programming problems for which the linear constraints
exhibit a (recursive) block-structure: The problem decomposes into independent and …

Parameterized algorithms for block-structured integer programs with large entries

J Cslovjecsek, M Koutecký, A Lassota, M Pilipczuk… - Proceedings of the 2024 …, 2024 - SIAM
We study two classic variants of block-structured integer programming. Two-stage stochastic
programs are integer programs of the form {A ix+ D iyi= bi for all i= 1,…, n}, where Ai and Di …

Empowering the configuration-IP: new PTAS results for scheduling with setup times

K Jansen, KM Klein, M Maack, M Rau - Mathematical Programming, 2022 - Springer
Integer linear programs of configurations, or configuration IPs, are a classical tool in the
design of algorithms for scheduling and packing problems where a set of items has to be …

Integer programs with bounded subdeterminants and two nonzeros per row

S Fiorini, G Joret, S Weltge, Y Yuditsky - Journal of the ACM, 2025 - dl.acm.org
We give a strongly polynomial-time algorithm for integer linear programs defined by integer
coefficient matrices whose subdeterminants are bounded by a constant and that contain at …

High-multiplicity N-fold IP via configuration LP

D Knop, M Koutecký, A Levin, M Mnich… - Mathematical programming, 2023 - Springer
N-fold integer programs (IPs) form an important class of block-structured IPs for which
increasingly fast algorithms have recently been developed and successfully applied. We …

[HTML][HTML] Integer programming in parameterized complexity: Five miniatures

T Gavenčiak, M Koutecký, D Knop - Discrete Optimization, 2022 - Elsevier
Powerful results from the theory of integer programming have recently led to substantial
advances in parameterized complexity. However, our perception is that, except for Lenstra's …

About the complexity of two-stage stochastic IPs

KM Klein - International Conference on Integer Programming and …, 2020 - Springer
We consider so called 2-stage stochastic integer programs (IPs) and their generalized form
of multi-stage stochastic IPs. A 2-stage stochastic IP is an integer program of the form\max …

Collapsing the tower—on the complexity of multistage stochastic IPs

KM Klein, J Reuter - ACM Transactions on Algorithms, 2024 - dl.acm.org
In this article, we study the computational complexity of solving a class of block structured
integer programs (IPs), the so-called multistage stochastic IPs. A multistage stochastic IP is …

The double exponential runtime is tight for 2-stage stochastic ILPs

K Jansen, KM Klein, A Lassota - Mathematical Programming, 2023 - Springer
We consider fundamental algorithmic number theoretic problems and their relation to a class
of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage …