Abstract
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.
The first author was supported by the grant projects GAČR 201/09/H012, GA UK 67410, SVV-2013-267317; the second author gratefully acknowledges support by the Natural Sciences and Engineering Research Council of Canada in the form of a Discovery Grant; the third and fourth were supported by ARC Discovery Project DP1094578; the first and fourth authors were also supported by the Fields Institute.
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Bulín, J., Delić, D., Jackson, M., Niven, T. (2013). On the Reduction of the CSP Dichotomy Conjecture to Digraphs. In: Schulte, C. (eds) Principles and Practice of Constraint Programming. CP 2013. Lecture Notes in Computer Science, vol 8124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40627-0_17
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DOI: https://doi.org/10.1007/978-3-642-40627-0_17
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