Related papers: Variable and value elimination in binary constrain…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
For an optimization problem $\Pi$ on graphs whose solutions are vertex sets, a vertex $v$ is called $c$-essential for $\Pi$ if all solutions of size at most $c \cdot OPT$ contain $v$. Recent work showed that polynomial-time algorithms to…
Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
In the Permutation Constraint Satisfaction Problem (Permutation CSP) we are given a set of variables $V$ and a set of constraints C, in which constraints are tuples of elements of V. The goal is to find a total ordering of the variables,…
In optimization problems involving smooth functions and real and matrix variables, that contain matrix semidefiniteness constraints, consider the following change of variables: Replace the positive semidefinite matrix $X \in \mathbb{S}^d$,…
We propose joinwidth, a new complexity parameter for the Constraint Satisfaction Problem (CSP). The definition of joinwidth is based on the arrangement of basic operations on relations (joins, projections, and pruning), which inherently…
Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing…
Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new…
For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every…
This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
A binary VCSP is a general framework for the minimization problem of a function represented as the sum of unary and binary cost functions. An important line of VCSP research is to investigate what functions can be solved in polynomial time.…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
We investigate the physical origins of multiple solutions to boundary value problems in the fully constrained MSSM and NMSSM. We derive mathematical criteria that formulate circumstances under which multiple solutions can appear. Finally,…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple…