相关论文: On the complexity of solving a decision problem wi…

In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP)…

It is a notorious open question whether integer programs (IPs), with an integer coefficient matrix $M$ whose subdeterminants are all bounded by a constant $\Delta$ in absolute value, can be solved in polynomial time. We answer this question…

The network-based study of financial systems has received considerable attention in recent years but has seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from the temporal point of view…

The Integer Programming Problem (IP) for a polytope P \subseteq R^n is to find an integer point in P or decide that P is integer free. We give an algorithm for an approximate version of this problem, which correctly decides whether P…

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…

We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow…

We consider the problem of learning Bayesian networks (BNs) from complete discrete data. This problem of discrete optimisation is formulated as an integer program (IP). We describe the various steps we have taken to allow efficient solving…

This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…

Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…

In project scheduling under processing times uncertainty, the Anchor-Robust Project Scheduling Problem is to find a baseline schedule of bounded makespan and a max-weight subset of jobs whose starting times are guaranteed. The problem was…

Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a…

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…

For a binary integer program (IP) ${\rm max} ~ c^\mathsf{T} x, Ax \leq b, x \in \{0,1\}^n$, where $A \in \mathbb{R}^{m \times n}$ and $c \in \mathbb{R}^n$ have independent Gaussian entries and the right-hand side $b \in \mathbb{R}^m$…

In the framework of Model Predictive Control (MPC), the control input is typically computed by solving optimization problems repeatedly online. For general nonlinear systems, the online optimization problems are non-convex and…

Influence Diagrams (ID) are a flexible tool to represent discrete stochastic optimization problems, including Markov Decision Process (MDP) and Partially Observable MDP as standard examples. More precisely, given random variables considered…

The challenging task of learning structures of probabilistic graphical models is an important problem within modern AI research. Recent years have witnessed several major algorithmic advances in structure learning for Bayesian…

This document presents an Integer Linear Programming (ILP) approach to optimize pedestrian evacuation in flood-prone historic urban areas. The model aims to minimize total evacuation cost by integrating pedestrian speed, route length, and…

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…

Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete…

We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…