Corpus ID: 12004276

Binarisation via Dualisation for Valued Constraints

  title={Binarisation via Dualisation for Valued Constraints},
  author={David A. Cohen and Martin C. Cooper and Peter Jeavons and Stanislav Živn{\'y}},
Constraint programming is a natural paradigm for many combinatorial optimisation problems. The complexity of constraint satisfaction for various forms of constraints has been widely-studied, both to inform the choice of appropriate algorithms, and to understand better the boundary between polynomial-time complexity and NP-hardness. In constraint programming it is well-known that any constraint satisfaction problem can be converted to an equivalent binary problem using the so-called dual… Expand
The Power of Sherali-Adams Relaxations for General-Valued CSPs
A precise algebraic characterization of the power of Sherali--Adams relaxations for solvability of valued constraint satisfaction problems (CSPs) to optimality is given and a dichotomy theorem for valued constraint languages that can express an injective unary function is obtained. Expand
Binarisation for Valued Constraint Satisfaction Problems
It is established that VCSPs over a fixed valued constraint language are polynomial-time equivalent to Minimum-Cost Homomorphism Problems over aFixed digraph. Expand
Complexity of Infinite-Domain Constraint Satisfaction
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O ct 2 01 5 Necessary Conditions for Tractability of Valued CSPs ∗
The connection between constraint languages and clone theory has been a fruitful line of research on the complexity of constraint satisfaction problems. In a recent result, Cohen et al. [SICOMP’13]Expand
A Model-Theoretic View on Qualitative Constraint Reasoning
A model-theoretic perspective on qualitative constraint reasoning is presented and the significance of omega-categoricity for qualitative reasoning, of primitive positive interpretations for complexity analysis, and of Datalog as a unifying language for describing local consistency algorithms are discussed. Expand
Graph Homomorphisms and Universal Algebra Course Notes
1 The Basics 2 1.1 Graphs and Digraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Graph Homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 TheExpand


Classifying the Complexity of Constraints Using Finite Algebras
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored. Expand
The Power of Linear Programming for Valued CSPs
This work obtains tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: sub modular on arbitrary lattices, bisubmodular on arbitrary finite domains, and weakly (and hence strongly) tree-sub modular on arbitrarily trees. Expand
Closure properties of constraints
This paper investigates the subclasses that arise from restricting the possible constraint types, and shows that any set of constraints that does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. Expand
Binary vs. non-binary constraints
A formal comparison of the dual transformation and the hidden transformation of constraint satisfaction problems with finite domains focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms. Expand
On digraph coloring problems and treewidth duality
  • Albert Atserias
  • Mathematics, Computer Science
  • 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
It is known that every constraint satisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem, and it is shown that it is semi-decidable, given H, whether the H-coloring problem is definable in full first-order logic. Expand
An Algebraic Theory of Complexity for Discrete Optimization
It is shown that the complexity of a finite-domain discrete optimization problem is determined by certain algebraic properties of the objective function, which are called weighted polymorphisms, and this approach is used to derive a complete classification of complexity for the Boolean case. Expand
The Expressive Power of Binary Submodular Functions
The results imply limitations on this kind of reduction and establish for the first time that it cannot be used in general to minimise arbitrary submodular functions. Expand
On the Reduction of the CSP Dichotomy Conjecture to Digraphs
A simple variant of such a reduction is presented and used to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. Expand
A finer reduction of constraint problems to digraphs
The Algebraic CSP dichotomy conjecture as well as the conjectures characterizing CSPs solvable in logspace and in nondeterministic logspace are equivalent to their restriction to digraphs. Expand
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory
This paper isolates a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit a dichotomy, and explains the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy. Expand