Related papers: On Planar Valued CSPs
We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…
The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template…
Let $D$, called the domain, be a fixed finite set and let $\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\to\mathbb{Q}\cup\{\infty\}$, where different functions might have different arity $m$.…
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity $k$ is…
A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…
We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use…
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…
We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper,…
In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAP-score, a version of the Shapley value that can help explain…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language, which is a fixed, finite set of relations over a finite domain D. An instance of the…
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.…
We show that various recent algorithms for finite-domain constraint satisfaction problems (CSP), which are based on solving their affine integer relaxations, do not solve all tractable and not even all Maltsev CSPs. This rules them out as…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…