Related papers: Solving Integer Linear Programs with a Small Numbe…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
Many fundamental 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 dimension of the program, and polynomial in the size of the ILP. That…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times.…
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…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
Answering science questions posed in natural language is an important AI challenge. Answering such questions often requires non-trivial inference and knowledge that goes beyond factoid retrieval. Yet, most systems for this task are based on…
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from…
Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on…
Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing…
The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed integer programming (MIP)…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on…
Many annotation problems in computer vision can be phrased as integer linear programs (ILPs). The use of standard industrial solvers does not to exploit the underlying structure of such problems eg, the skeleton in pose estimation. The…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
In this paper, we present FPT-algorithms for special cases of the shortest vector problem (SVP) and the integer linear programming problem (ILP), when matrices included to the problems' formulations are near square. The main parameter is…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…