相关论文: A Characterisation of First-Order Constraint Satis…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
We present the finite first-order theory (FFOT) machine, which provides an atemporal description of computation. We then develop a concept of complexity for the FFOT machine, and prove that the class of problems decidable by a FFOT machine…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the…
Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…
We provide an internal characterization of those finite algebras (i.e., algebraic structures) $\mathbf A$ such that the number of homomorphisms from any finite algebra $\mathbf X$ to $\mathbf A$ is bounded from above by a polynomial in the…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…
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…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
We present a structural classification of constraint satisfaction problems (CSP) described by reflexive complete $2$-edge-coloured graphs. In particular, this classification extends the structural dichotomy for graph homomorphism problems…