Related papers: Parameterized algorithms for block-structured inte…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
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 exact solutions when some part of the input is a fixed parameter.…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…
We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times…
In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax <= b. We give a fixed…
In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed {\em n-fold integer programming problems} are polynomial time solvable. Our proof involves two heavy ingredients…
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 parameter $A$, dimension $n$, and numerical data of binary…
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 $A$: its numeric measure $a$ and its sparsity measure $d$. We…
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 "$n$-fold integer programs" which recently received…
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 \{ c^T x \mid Ax = b, l \leq x \leq u, x \in…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…
We consider the problem of solving integer programs of the form $\min \{\,c^\intercal x\ \colon\ Ax=b, x\geq 0\}$, where $A$ is a multistage stochastic matrix in the following sense: the primal treedepth of $A$ is bounded by a parameter…
A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes.…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…