Related papers: Local consistency as a reduction between constrain…
In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language $\Gamma$ is tractable if and only if $\Gamma$ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…
We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras…
Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework,…
One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs…
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…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
Concepts of consistency have long played a key role in constraint programming but never developed in integer programming (IP). Consistency nonetheless plays a role in IP as well. For example, cutting planes can reduce backtracking by…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…