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The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to…
We study the computational complexity of exact minimisation of rational-valued discrete functions. Let $\Gamma$ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
We develop an analytical framework for Boolean Promise Constraint Satisfaction Problems (PCSPs) that studies polymorphisms through the notion of influence from Fourier analysis of Boolean functions. Extending the work of Brakensiek,…
A Datalog program solves a constraint satisfaction problem (CSP) if and only if it derives the goal predicate precisely on the unsatisfiable instances of the CSP. There are three Datalog fragments that are particularly important for…
Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…
Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment,…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint…
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 show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
Holant problems are a general framework to study the computational complexity of counting problems. It is a more expressive framework than counting constraint satisfaction problems (CSP) which are in turn more expressive than counting graph…
The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…
Mermin and Peres showed that there are boolean constraint systems (BCSs) which are not satisfiable, but which are satisfiable with quantum observables. This has led to a burgeoning theory of quantum satisfiability for constraint systems,…
In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from…
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…