144 research outputs found
On the reduction of the CSP dichotomy conjecture to digraphs
It is well known that the constraint satisfaction problem over general
relational structures can be reduced in polynomial time to digraphs. We present
a simple variant of such a reduction and use it to show that the algebraic
dichotomy conjecture is equivalent to its restriction to digraphs and that the
polynomial reduction can be made in logspace. We also show that our reduction
preserves the bounded width property, i.e., solvability by local consistency
methods. We discuss further algorithmic properties that are preserved and
related open problems.Comment: 34 pages. Article is to appear in CP2013. This version includes two
appendices with proofs of claims omitted from the main articl
Algebra and the Complexity of Digraph CSPs: a Survey
We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems
Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem
The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction
Problem over a fixed template is solvable in polynomial time if the algebra of
polymorphisms associated to the template lies in a Taylor variety, and is
NP-complete otherwise. This paper provides two new characterizations of
finitely generated Taylor varieties. The first characterization is using
absorbing subalgebras and the second one cyclic terms. These new conditions
allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the
authors) and the characterization of locally finite Taylor varieties using weak
near-unanimity terms (proved by McKenzie and Mar\'oti) in an elementary and
self-contained way
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