A. Atserias, A. A. Bulatov, and V. Dalmau, On the Power of k-Consistency, Proc. ICALP'07, pp.279-290, 2007.
DOI : 10.1007/978-3-540-73420-8_26

L. Barto, Abstract, The Bulletin of Symbolic Logic, vol.34, issue.03, pp.14-24, 2014.
DOI : 10.1090/S0002-9947-09-04874-0

L. Barto and M. Kozik, Constraint Satisfaction Problems Solvable by Local Consistency Methods, Journal of the ACM, vol.61, issue.1, 2014.
DOI : 10.1142/S021819670900524X

C. Bessì-ere, J. Régin, R. H. Yap, and Y. Zhang, An optimal coarse-grained arc consistency algorithm, Artificial Intelligence, vol.165, issue.2, pp.165-185, 2005.
DOI : 10.1016/j.artint.2005.02.004

A. Bulatov, Combinatorial problems raised from 2-semilattices, Journal of Algebra, vol.298, issue.2, pp.321-339, 2006.
DOI : 10.1016/j.jalgebra.2004.07.044
URL : https://doi.org/10.1016/j.jalgebra.2004.07.044

A. Bulatov, Bounded relational width. Unpublished manuscript, 2009.

A. Bulatov and V. Dalmau, A Simple Algorithm for Mal'tsev Constraints, SIAM Journal on Computing, vol.36, issue.1, pp.16-27, 2006.
DOI : 10.1137/050628957

C. Carbonnel and M. C. Cooper, Tractability in constraint satisfaction problems: a survey, Constraints, vol.13, issue.1???2, pp.115-144, 2016.
DOI : 10.1007/s10601-007-9033-9
URL : https://hal.archives-ouvertes.fr/hal-01230685

D. A. Cohen, M. C. Cooper, P. G. Jeavons, and A. A. Krokhin, The complexity of soft constraint satisfaction, Artificial Intelligence, vol.170, issue.11, pp.983-1016, 2006.
DOI : 10.1016/j.artint.2006.04.002

D. A. Cohen, M. C. Cooper, P. Creed, D. Marx, and A. Z. Salamon, The tractability of CSP classes defined by forbidden patterns, Journal of Artificial Intelligence Research, vol.45, pp.47-78, 2012.

D. A. Cohen, M. C. Cooper, G. Escamocher, S. Zivn´yzivn´y, and S. Zivn´yzivn´y, Variable and value elimination in binary constraint satisfaction via forbidden patterns, Proc. IJCAI'15, pp.1127-1143, 2015.
DOI : 10.1016/j.jcss.2015.02.001
URL : https://hal.archives-ouvertes.fr/hal-01280349

M. C. Cooper, Linear-time algorithms for testing the realisability of line drawings of curved objects, Artificial Intelligence, vol.108, issue.1-2, pp.31-67, 1999.
DOI : 10.1016/S0004-3702(98)00118-0

M. C. Cooper and G. Escamocher, Characterising the complexity of constraint satisfaction problems defined by 2-constraint forbidden patterns, Discrete Applied Mathematics, vol.184, pp.89-113, 2015.
DOI : 10.1016/j.dam.2014.10.035
URL : https://hal.archives-ouvertes.fr/hal-01283864

M. C. Cooper, S. De-givry, M. Sánchez, T. Schiex, M. Zytnicki et al., Soft arc consistency revisited, Artificial Intelligence, vol.174, issue.7-8, pp.7-8449, 2010.
DOI : 10.1016/j.artint.2010.02.001
URL : https://doi.org/10.1016/j.artint.2010.02.001

M. C. Cooper, P. G. Jeavons, and A. Z. Salamon, Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination, Artificial Intelligence, vol.174, issue.9-10, pp.9-10570, 2010.
DOI : 10.1016/j.artint.2010.03.002
URL : https://doi.org/10.1016/j.artint.2010.03.002

M. C. Cooper, A. Mouelhi, C. Terrioux, and B. Zanuttini, On Broken Triangles, Proc. CP'14, pp.9-24, 2014.
DOI : 10.1007/978-3-319-10428-7_5
URL : https://hal.archives-ouvertes.fr/hal-01356058

M. C. Cooper, P. Jégou, and C. Terrioux, A Microstructure-Based Family of Tractable Classes for CSPs, Proc. CP'15, pp.74-88, 2015.
DOI : 10.1007/978-3-319-23219-5_6
URL : https://hal.archives-ouvertes.fr/hal-01343050

M. C. Cooper and S. Zivn´yzivn´y, The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, 2016.
DOI : 10.1145/2974019
URL : https://hal.archives-ouvertes.fr/hal-01671341

V. Dalmau, Generalized Majority-Minority Operations are Tractable, Logical Methods in Computer Science, vol.2, issue.4, 2006.
DOI : 10.2168/LMCS-2(4:1)2006

R. Dechter, I. Meiri, and J. Pearl, Temporal constraint networks, Temporal Constraint Networks, pp.61-95, 1991.
DOI : 10.1016/0004-3702(91)90006-6

G. Escamocher, Forbidden Patterns in Constraint Satisfaction Problems, 2014.

T. Feder and M. Y. Vardi, The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory, SIAM Journal on Computing, vol.28, issue.1, pp.57-104, 1998.
DOI : 10.1137/S0097539794266766

J. Gao, M. Yin, and J. Zhou, Hybrid tractable classes of binary quantified constraint satisfaction problems, Proc. AAAI'11, 2011.

M. J. Green and D. A. Cohen, Domain permutation reduction for constraint satisfaction problems, Artificial Intelligence, vol.172, issue.8-9, pp.1094-1118, 2008.
DOI : 10.1016/j.artint.2007.12.001
URL : https://doi.org/10.1016/j.artint.2007.12.001

. Grohe, The complexity of homomorphism and constraint satisfaction problems seen from the other side, Journal of the ACM, vol.54, issue.1, pp.1-24, 2007.
DOI : 10.1145/1206035.1206036

M. Idziak, P. Markovic, R. Mckenzie, M. Valeriote, and R. Willard, Tractability and Learnability Arising from Algebras with Few Subpowers, SIAM Journal on Computing, vol.39, issue.7, pp.3023-3037, 2010.
DOI : 10.1137/090775646
URL : http://www.math.mcmaster.ca/~matt/publications/valeriote-fewsubpowers.pdf

P. G. Jeavons and M. C. Cooper, Tractable constraints on ordered domains, Artificial Intelligence, vol.79, issue.2, pp.327-339, 1995.
DOI : 10.1016/0004-3702(95)00107-7
URL : https://doi.org/10.1016/0004-3702(95)00107-7

V. Kolmogorov, M. Rolínek, and R. Takhanov, Effectiveness of Structural Restrictions for Hybrid CSPs, 1504.
DOI : 10.1007/s00012-010-0082-3

V. Kolmogorov, J. Thapper, and S. Zivn´yzivn´y, The Power of Linear Programming for General-Valued CSPs, SIAM Journal on Computing, vol.44, issue.1, pp.1-36, 2015.
DOI : 10.1137/130945648

. Marx, Tractable hypergraph properties for constraint satisfaction and conjunctive queries, Journal of the ACM, vol.60, issue.6
DOI : 10.1145/1806689.1806790
URL : http://arxiv.org/pdf/0911.0801

W. Naanaa, Unifying and extending hybrid tractable classes of CSPs, Journal of Experimental & Theoretical Artificial Intelligence, vol.27, issue.4, pp.407-424, 2013.
DOI : 10.1145/263867.263499

R. Takhanov, Hybrid (V)CSPs and algebraic reductions. CoRR, abs, 1506.

J. Thapper and S. Zivn´yzivn´y, The complexity of finite-valued CSPs, J.ACM. To appear