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.
KeywordsPolynomial Time Relational Structure Constraint Satisfaction Problem Single Edge Relation Symbol
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- 3.Barto, L., Kozik, M., Niven, T.: The CSP dichotomy holds for digraphs with no sources and no sinks (a positive answer to a conjecture of Bang-Jensen and Hell). SIAM J. Comput. 38(5), 1782–1802 (2008/2009), http://dx.doi.org/10.1137/070708093
- 8.Feder, T., Vardi, M.Y.: The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM J. Comput. 28(1), 57–104 (electronic) (1999), http://dx.doi.org/10.1137/S0097539794266766
- 10.Hell, P., Nešetřil, J.: Graphs and homomorphisms. Oxford Lecture Series in Mathematics and its Applications, vol. 28. Oxford University Press, Oxford (2004), http://dx.doi.org/10.1093/acprof:oso/9780198528173.001.0001 CrossRefzbMATHGoogle Scholar
- 12.Jackson, M., Kowalski, T., Niven, T.: Digraph related constructions and the complexity of digraph homomorphism problems. arXiv:1304.4986 [math.CO] (2013)Google Scholar
- 19.Schaefer, T.J.: The complexity of satisfiability problems. In: Conference Record of the Tenth Annual ACM Symposium on Theory of Computing (San Diego, Calif., 1978), pp. 216–226. ACM, New York (1978)Google Scholar