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 …

A parameterized strongly polynomial algorithm for block structured integer programs

M Koutecký, A Levin, S Onn - arXiv preprint arXiv:1802.05859, 2018 - arxiv.org
The theory of $ n $-fold integer programming has been recently emerging as an important
tool in parameterized complexity. The input to an $ n $-fold integer program (IP) consists of …

Scheduling meets n-fold integer programming

D Knop, M Koutecký - Journal of Scheduling, 2018 - Springer
Scheduling problems are fundamental in combinatorial optimization. Much work has been
done on approximation algorithms for NP-hard cases, but relatively little is known about …

Combinatorial n-fold integer programming and applications

D Knop, M Koutecký, M Mnich - Mathematical Programming, 2020 - Springer
Many fundamental NP NP-hard problems can be formulated as integer linear programs
(ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the …

[PDF][PDF] Winner Robustness via Swap-and Shift-Bribery: Parameterized Counting Complexity and Experiments.

N Boehmer, R Bredereck, P Faliszewski… - IJCAI, 2021 - comsoc-community.org
We study the parameterized complexity of counting variants of Swap-and Shift-Bribery,
focusing on the parameterizations by the number of swaps and the number of voters. Facing …

Faster algorithms for integer programs with block structure

F Eisenbrand, C Hunkenschröder, KM Klein - arXiv preprint arXiv …, 2018 - arxiv.org
We consider integer programming problems $\max\{c^ T x:\mathcal {A} x= b, l\leq x\leq u,
x\in\mathbb {Z}^{nt}\} $ where $\mathcal {A} $ has a (recursive) block-structure generalizing" …

Opinion diffusion and campaigning on society graphs

P Faliszewski, R Gonen, M Koutecký… - Journal of Logic and …, 2022 - academic.oup.com
We study the effects of campaigning, where the society is partitioned into voter clusters and
a diffusion process propagates opinions in a network connecting the clusters. Our model can …

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 …

Tight complexity lower bounds for integer linear programming with few constraints

D Knop, M Pilipczuk, M Wrochna - ACM Transactions on Computation …, 2020 - dl.acm.org
We consider the standard ILP Feasibility problem: given an integer linear program of the
form {A x= b, x⩾ 0}, where A is an integer matrix with k rows and ℓ columns, x is a vector of ℓ …

Robustness of participatory budgeting outcomes: complexity and experiments

N Boehmer, P Faliszewski, Ł Janeczko… - … on Algorithmic Game …, 2023 - Springer
We study the robustness of approval-based participatory budgeting (PB) rules to random
noise in the votes. First, we analyze the computational complexity of the# Flip-Bribery …