Related papers: Parity Polytopes and Binarization
We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the…
We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a…
Let X be the set of integer points in some polyhedron. We investigate the smallest number of facets of any polyhedron whose set of integer points is X. This quantity, which we call the relaxation complexity of X, corresponds to the smallest…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…
In this article we address the problem of partitioning a carsharing business area into pricing zones. We formalize the problem mathematically and show that the resulting partitioning problem can be formulated as a binary integer programming…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean literals. One of the popular, efficient ideas used to solve PB-problems (a set of PB-constraints) is to translate them to SAT instances (encodings) via, for…
Statistical algorithms are usually helping in making decisions in many aspects of our lives. But, how do we know if these algorithms are biased and commit unfair discrimination of a particular group of people, typically a minority?…
While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…
Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…