The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom
arXiv:2008.11943 · doi:10.1613/jair.1.14195
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 Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.
32 pages, 2 figures
References in corpus (5)
- All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
- Canonical Functions: a proof via topological dynamics
- Algebraic foundations for qualitative calculi and networks
- Smooth approximations and CSPs over finitely bounded homogeneous structures
- The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom