A Proof of CSP Dichotomy Conjecture
Dmitriy Zhuk
- pp 331-342
Reads0
Chats0
TLDR
In this article, it was conjectured that if a core of a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, unless it is NP-complete.Abstract:
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 standard way to parametrize interesting subclasses of the constraint satisfaction problem is via finite constraint languages. The main problem is to classify those subclasses that are solvable in polynomial time and those that are NP-complete. It was conjectured that if a core of a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, otherwise it is NP-complete.In the paper we present an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture.read more
Citations
More filters
Journal ArticleDOI
A Proof of the CSP Dichotomy Conjecture
TL;DR: This article presents an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture.
Journal ArticleDOI
Equations in oligomorphic clones and the constraint satisfaction problem for ω-categorical structures
TL;DR: It is proved that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a non-trivial system of linear identities, and obtain non-Trivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset.
Proceedings ArticleDOI
A universal-algebraic proof of the complexity dichotomy for Monotone Monadic SNP
TL;DR: In this paper, a new proof of the reduction to finite-domain CSPs that does not rely on the results of Kun is presented, which allows us to obtain a stronger statement and to verify the Bodirsky-Pinsker dichotomy conjecture for CSP in MMSNP.
Journal ArticleDOI
Algebraic approach to promise constraint satisfaction
TL;DR: A new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem are introduced, and it is shown that every PCSP with a fixed constraint language is equivalent to a problem of this form.
Journal ArticleDOI
Discrete Temporal Constraint Satisfaction Problems
TL;DR: It is proved that every discrete temporal CSP is in P or NP-complete, unless it can be formulated as a finite domain CSP, in which case the computational complexity is not known in general.
References
More filters
Journal ArticleDOI
Consistency in Networks of Relations
TL;DR: The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency algorithm, to discuss their relationships and the may applications, both realized and potential of network consistency algorithms.
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
Networks of constraints: Fundamental properties and applications to picture processing
TL;DR: Constraints are treated algebraically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network, and this solution is proved exact in special cases, e.g., for tree-like and series-parallel networks and for classes of relations for which a distributive property holds.
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.