Related papers: Parity Polytopes and Binarization
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…
We prove that any mixed-integer linear extended formulation for the matching polytope of the complete graph on $n$ vertices, with a polynomial number of constraints, requires $\Omega(\sqrt{\sfrac{n}{\log n}})$ many integer variables. By…
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…
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…
We investigate the fine-grained and the parameterized complexity of several generalizations of binary constraint satisfaction problems (BINARY-CSPs), that subsume variants of graph colouring problems. Our starting point is the observation…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We study the problem of abstracting a table of data about individuals so that no selection query can identify fewer than k individuals. We show that it is impossible to achieve arbitrarily good polynomial-time approximations for a number of…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In…
Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
Anti-unification in logic programming refers to the process of capturing common syntactic structure among given goals, computing a single new goal that is more general called a generalization of the given goals. Finding an arbitrary common…