Abstract
We study the (non-uniform) quantified constraint satisfaction problem QCSP\((\mathcal{H})\) as \(\mathcal{H}\) ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP\((\mathcal{H})\) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of \(\mathcal{H}\) to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP\((\mathcal{H})\) is either in NL or is Pspace-complete.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bandelt, H.J., Dhlmann, A., Schtte, H.: Absolute retracts of bipartite graphs. Discrete Applied Mathematics 16(3), 191–215 (1987)
Bandelt, H.-J., Pesch, E.: Dismantling absolute retracts of reflexive graphs. Eur. J. Comb. 10, 211–220 (1989)
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 Journal on Computing 38(5), 1782–1802 (2009)
Börner, F., Bulatov, A.A., Chen, H., Jeavons, P., Krokhin, A.A.: The complexity of constraint satisfaction games and qcsp. Inf. Comput. 207(9), 923–944 (2009)
Börner, F., Krokhin, A., Bulatov, A., and Jeavons, P. Quantified constraints and surjective polymorphisms. Tech. Rep. PRG-RR-02-11, Oxford University (2002)
Bulatov, A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. J. ACM 53(1), 66–120 (2006)
Bulatov, A., Krokhin, A., Jeavons, P.G.: Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing 34, 720–742 (2005)
Chen, H.: The complexity of quantified constraint satisfaction: Collapsibility, sink algebras, and the three-element case. SIAM J. Comput. 37(5), 1674–1701 (2008)
Chen, H., Madelaine, F., Martin, B.: Quantified constraints and containment problems. In: 23rd Annual IEEE Symposium on Logic in Computer Science, pp. 317–328 (2008)
Dalmau, V., Krokhin, A.A.: Majority constraints have bounded pathwidth duality. Eur. J. Comb. 29(4), 821–837 (2008)
Feder, T., Vardi, M.: The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory. SIAM Journal on Computing 28, 57–104 (1999)
Golovach, P., Paulusma, D., Song, J.: Computing vertex-surjective homomorphisms to partially reflexive trees. In: Kulikov, A., Vereshchagin, N. (eds.) CSR 2011. LNCS, vol. 6651. Springer, Heidelberg (to appear, 2011)
Hell, P., Nešetřil, J.: On the complexity of H-coloring. Journal of Combinatorial Theory, Series B 48, 92–110 (1990)
Martin, B., Madelaine, F.: Towards a trichotomy for quantified H-coloring. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 342–352. Springer, Heidelberg (2006)
Patrignani, M., Pizzonia, M.: The complexity of the matching-cut problem. In: Brandstädt, A., Le, V.B. (eds.) WG 2001. LNCS, vol. 2204, pp. 284–295. Springer, Heidelberg (2001)
Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of STOC 1978, pp. 216–226 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martin, B. (2011). QCSP on Partially Reflexive Forests. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-23786-7_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23785-0
Online ISBN: 978-3-642-23786-7
eBook Packages: Computer ScienceComputer Science (R0)