A New Combinatorial Approach to the Constraint Satisfaction Problem Dichotomy Classification
نویسندگان
چکیده
We introduce a new general polynomial-time constructionthe fibre constructionwhich reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P ), where P is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that CSP(P ) is NP -complete for any subprojective (and so for any projective) relational structure. The fibre construction allows us to prove the NP -completeness part of the conjectured Dichotomy Classification of CSPs, previously obtained by algebraic methods. We show that this conjectured Dichotomy Classification is equivalent to the dichotomy of whether or not the template is subprojective. This approach is flexible enough to yield NP -completeness of coloring problems with large girth and bounded degree restrictions thus reducing the Feder-Hell-Huang and Kostočka-NešeťrilSmoĺıková problems to the Dichotomy Classification of coloring problems.
منابع مشابه
Combinatorial Proof that Subprojective Constraint Satisfaction Problems are NP-Complete
We introduce a new general polynomial-time constructionthe fibre constructionwhich reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is any subprojective relational system. As a consequence we get a new proof (not using universal algebra) that CSP(P) is NP -complete for any subprojective (and thus also projective) relational system. The fi...
متن کاملA combinatorial constraint satisfaction problem dichotomy classification conjecture
We further generalise a construction – the fibre construction – that was developed in an earlier paper of the first two authors. The extension in this paper gives a polynomial-time reduction of CSP(H) for any relational system H to CSP(P ) for any relational system P that meets a certain technical partition condition, that of being K3-partitionable. Moreover, we define an equivalent condition o...
متن کاملDichotomy theorem for general Minimum Cost Homomorphisms Problem
In the classical Constraint Satisfaction Problem(CSP ) two finite models are given and we are asked to find their homomorphism. In the MinHom problem, besides the models, a set of weighted pairs of elements of this two models is given and the task is to find a homomorphism that maximizes the weight of pairs consistent with the homomorphism, i.e. pairs for which homomorphism maps the first eleme...
متن کاملA Complexity Dichotomy for Poset Constraint Satisfaction
We determine the complexity of all constraint satisfaction problems over partial orders, in particular we show that every such problem is NP-complete or can be solved in polynomial time. This result generalises the complexity dichotomy for temporal constraint satisfaction problems by Bodirsky and Kára. We apply the so called universal-algebraic approach together with tools from model theory and...
متن کاملClassifying the Complexity of Constraints Using Finite Algebras
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. Here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the com...
متن کامل