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
When symmetries are not enough: a hierarchy of hard Constraint Satisfaction Problems.
TL;DR: A model-theoretic construction -- a refinement of the Hrushosvki-encoding -- is applied to $\omega$-categorical structures, showing that the encoded structures retain desirable algebraic properties, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly behaved in terms of computational complexity.
Journal ArticleDOI
ω-categorical structures avoiding height 1 identities
TL;DR: The algebraic dichotomy conjecture for constraint satisfaction problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures was studied in this paper.
Journal ArticleDOI
Dichotomies in Ontology-Mediated Querying with the Guarded Fragment
TL;DR: In this paper, the authors study ontology-mediated querying in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries, and classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O.
Posted Content
When is Approximate Counting for Conjunctive Queries Tractable
TL;DR: The first FPRAS and polynomial time sampler for the set of trees of size n accepted by a tree automaton is demonstrated, which improves the prior quasi-polynomial time randomized approximation scheme (QPRAS) and sampling algorithm of Gore, Jerrum, Kannan, Sweedyk, and Mahaney ’97.
Proceedings ArticleDOI
Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems)
TL;DR: The algebraic dichotomy conjecture for constraint satisfaction problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures was studied in this paper.
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