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arXiv · 2008.11943

The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

Manuel Bodirsky·Simon Knäuer
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Abstract

Robin Hirsch posed in 1996 the 'Really Big Complexity Problem': classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a flexible atom; in this case, the problem is NP-complete or in P. The classification task can be reduced to the case where A is integral. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Ne\v{s}et\v{r}il and R\"odl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.

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BibTeXRIS

Manuel Bodirsky, Simon Knäuer. 2020-08-27. The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom. https://doi.org/10.1613/jair.1.14195

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