A Dichotomy Theorem for Nonuniform CSPs
Andrei A. Bulatov
- pp 319-330
Reads0
Chats0
TLDR
In this paper, the authors confirm the Dichotomy Conjecture for the non-uniform CSP, which states that for every constraint language \Gm the problem is either solvable in polynomial time or is NP-complete.Abstract:
In a non-uniform Constraint Satisfaction problem CSP(Γ), where G is a set of relations on a finite set A, the goal is to find an assignment of values to variables subject to constraints imposed on specified sets of variables using the relations from Γ. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP(Γ) is either solvable in polynomial time or is NP-complete. It was proposed by Feder and Vardi in their seminal 1993 paper. In this paper we confirm the Dichotomy Conjecture.read more
Citations
More filters
Posted Content
Local structure of idempotent algebras II
TL;DR: It is demonstrated that the edges of the graph of an algebra omitting type 1 can be made `thin', that is, there are term operations that behave very similar to semilattice, majority, or affine operations on 2-element subsets of the algebra.
Proceedings ArticleDOI
Approximate Graph Colouring and Crystals
Lorenzo Ciardo,Stanislav Živný +1 more
TL;DR: It is shown that approximate graph colouring is not solved by any level of the affine integer programming (AIP) hierarchy, and a combinatorial characterisation is provided for realisable systems of tensors; i.e., sets of low-dimensional tensors that can be realised as the projections of a single high-dimensional Tensor.
Book ChapterDOI
Finite Relation Algebras with Normal Representations
TL;DR: The present article translates the recent findings into the traditional relation algebra setting, and points out a series of open problems at the interface between model theory and the theory of relation algebras.
Journal ArticleDOI
Functorial Question Answering
TL;DR: This work studies the relational variant of the categorical compositional distributional models of Coecke et al, where it shows that RelCoCat models factorise through Cartesian bicategories, and defines question answering as an NP-complete problem.
Proceedings ArticleDOI
Canonical polymorphisms of ramsey structures and the unique interpolation property
Manuel Bodirsky,Bertalan Bodor +1 more
TL;DR: In this article, a polynomial-time tractability result for constraint satisfaction problems for first-order reducts of finitely bounded homogeneous structures has been obtained for the RCC5 spatial reasoning formalism.
References
More filters
Proceedings ArticleDOI
The complexity of satisfiability problems
TL;DR: An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
Journal ArticleDOI
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory
Tomás Feder,Moshe Y. Vardi +1 more
TL;DR: 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.
Journal ArticleDOI
On the complexity of H -coloring
Pavol Hell,Jaroslav Nešetřil +1 more
TL;DR: The natural conjecture, formulated in several sources, asserts that the H-coloring problem is NP-complete for any non-bipartite graph H, and a proof of this conjecture is given.
Journal ArticleDOI
Classifying the Complexity of Constraints Using Finite Algebras
TL;DR: 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.
Journal ArticleDOI
Undirected connectivity in log-space
TL;DR: A deterministic, log-space algorithm that solves st-connectivity in undirected graphs and implies a way to construct in log- space a fixed sequence of directions that guides a deterministic walk through all of the vertices of any connected graph.
Related Papers (5)
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory
Tomás Feder,Moshe Y. Vardi +1 more