S. Arnborg, D. Corneil, and A. Proskuroswki, -Tree, SIAM Journal on Algebraic Discrete Methods, vol.8, issue.2, pp.277-284, 1987.
DOI : 10.1137/0608024

C. Berge, Graphs and Hypergraphs, 1973.

C. Bessì-ere, P. Meseguer, E. C. Freuder, and J. Larrosa, On forward checking for non-binary constraint satisfaction, Artificial Intelligence, vol.141, issue.1-2, pp.205-224, 2002.
DOI : 10.1016/S0004-3702(02)00263-1

C. Bessì-ere and J. C. Régin, Refining the Basic Constraint Propagation Algorithm, Proceedings of IJCAI, pp.309-315, 2001.

F. Boussemart, F. Hemery, C. Lecoutre, and L. Sais, Boosting systematic search by weighting constraints, Proceedings of ECAI, pp.146-150, 2004.

C. Cabon, S. De-givry, L. Lobjois, T. Schiex, and J. P. Warners, Radio Link Frequency Assignment, Constraints, vol.4, issue.1, pp.79-89, 1999.
DOI : 10.1023/A:1009812409930

R. Dechter, Constraint processing, 2003.

R. Dechter and Y. E. Fattah, Topological parameters for time-space tradeoff, Artificial Intelligence, vol.125, issue.1-2, pp.93-118, 2001.
DOI : 10.1016/S0004-3702(00)00050-3
URL : https://doi.org/10.1016/s0004-3702(00)00050-3

R. Dechter and R. Mateescu, The Impact of AND/OR Search Spaces on Constraint Satisfaction and Counting, Proceedings of the 10th International Conference on Principles and Practice of Constraint Programming (CP), pp.731-736, 2004.
DOI : 10.1007/978-3-540-30201-8_56

R. Dechter and R. Mateescu, AND/OR search spaces for graphical models, Artificial Intelligence, vol.171, issue.2-3, pp.73-106, 2007.
DOI : 10.1016/j.artint.2006.11.003

R. Dechter and J. Pearl, Tree clustering for constraint networks, Artificial Intelligence, vol.38, issue.3, pp.353-366, 1989.
DOI : 10.1016/0004-3702(89)90037-4

A. Dermaku, T. Ganzow, G. Gottlob, B. J. Mcmahan, N. Musliu et al., Heuristic Methods for Hypertree Decomposition, Proceedings of MICAI, pp.1-11, 2008.
DOI : 10.1016/0196-6774(86)90023-4

R. Diestel and M. Müller, Connected tree-width. arXiv 1211, pp.7353-7355, 2014.
DOI : 10.1007/s00493-016-3516-5

A. Favier, S. De-givry, and P. Jégou, Exploiting Problem Structure for Solution Counting, Proceedings of CP, pp.335-343, 2009.
DOI : 10.1007/11499107_24
URL : http://www.inra.fr/bia/T/degivry/Favier09a.pdf

P. Fraigniaud and N. Nisse, Connected Treewidth and Connected Graph Searching, Proceedings of LATIN, pp.479-490, 2006.
DOI : 10.1007/978-3-540-30551-4_77
URL : https://hal.archives-ouvertes.fr/inria-00423448

E. Freuder, A Sufficient Condition for Backtrack-Free Search, Journal of the ACM, vol.29, issue.1, pp.24-32, 1982.
DOI : 10.1145/322290.322292
URL : http://www.cs.cmu.edu/~./arielpro/mfai_papers/jacm82.pdf

F. Gavril, Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph, SIAM Journal on Computing, vol.1, issue.2, pp.180-187, 1972.
DOI : 10.1137/0201013

M. Golumbic, Algorithmic Graph Theory and Perfect Graphs, 1980.

C. P. Gomes, B. Selman, N. Crato, and H. A. Kautz, Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems, Journal of Automated Reasoning, vol.24, issue.1/2, pp.67-100, 2000.
DOI : 10.1023/A:1006314320276

G. Gottlob, N. Leone, and F. Scarcello, A comparison of structural CSP decomposition methods, Artificial Intelligence, vol.124, issue.2, pp.243-282, 2000.
DOI : 10.1016/S0004-3702(00)00078-3

M. Gyssens, P. Jeavons, and D. Cohen, Decomposing constraint satisfaction problems using database techniques, Artificial Intelligence, vol.66, issue.1, pp.57-89, 1994.
DOI : 10.1016/0004-3702(94)90003-5
URL : http://www.cyberband.rhbnc.ac.uk/research/constraints/publications/pubs-ps/decomposing.ps

M. Hamann and D. Weißauer, Bounding Connected Tree-Width, SIAM Journal on Discrete Mathematics, vol.30, issue.3, 2015.
DOI : 10.1137/15M1044618
URL : http://arxiv.org/pdf/1503.01592

W. D. Harvey, Nonsystematic backtracking search, 1995.

P. Jégou, S. N. Ndiaye, and C. Terrioux, Computing and exploiting treedecompositions for solving constraint networks, Proceedings of CP, pp.777-781, 2005.

P. Jégou, S. N. Ndiaye, and C. Terrioux, An Extension of Complexity Bounds and Dynamic Heuristics for Tree-Decompositions of CSP, Proceedings of CP, pp.741-745, 2006.
DOI : 10.1007/11889205_62

P. Jégou, S. N. Ndiaye, and C. Terrioux, Dynamic Heuristics for Backtrack Search on Tree-Decomposition of CSPs, Proceedings of IJCAI, pp.112-117, 2007.

P. Jégou, S. N. Ndiaye, and C. Terrioux, Dynamic Management of Heuristics for Solving Structured CSPs, Proceedings of CP, pp.364-378, 2007.
DOI : 10.1007/978-3-540-74970-7_27

P. Jégou and C. Terrioux, Hybrid backtracking bounded by tree-decomposition of constraint networks, Artificial Intelligence, vol.146, issue.1, pp.43-75, 2003.
DOI : 10.1016/S0004-3702(02)00400-9

P. Jégou and C. Terrioux, Combining restarts, nogoods and decompositions for solving csps, Proceedings of ECAI, pp.465-470, 2014.

P. Jégou and C. Terrioux, Tree-Decompositions with Connected Clusters for Solving Constraint Networks, Proceedings of CP, pp.407-423, 2014.
DOI : 10.1007/978-3-319-10428-7_31

S. Karakashian, R. Woodward, and B. Y. Choueiry, Improving the Performance of Consistency Algorithms by Localizing and Bolstering Propagation in a Tree Decomposition, Proceedings of AAAI, pp.466-473, 2013.

U. Kjaerulff, Triangulation of Graphs -Algorithms Giving Small Total State Space, Tech. rep., Judex R.R. Aalborg, p.Denmark, 1990.

C. Lecoutre, Constraint Networks -Techniques and Algorithms, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00870016

C. Lecoutre, L. Sa¨?ssa¨?s, S. Tabary, and V. Vidal, Recording and Minimizing Nogoods from Restarts, JSAT, vol.1, pp.3-4, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00191092

M. Luby, A. Sinclair, and D. Zuckerman, Optimal speedup of Las Vegas algorithms, Information Processing Letters, vol.47, issue.4, pp.173-180, 1993.
DOI : 10.1016/0020-0190(93)90029-9

M. Müller, Connected tree-width. arXiv 1211, 2012.

B. Nadel, Tree Search and ARC Consistency in Constraint Satisfaction Algorithms, Search in Artificial Intelligence, pp.287-342, 1988.
DOI : 10.1007/978-1-4613-8788-6_9

J. Petke, On the bridge between Constraint Satisfaction and Boolean Satisfiability, 2012.
DOI : 10.1007/978-3-319-21810-6

N. Robertson and P. Seymour, Graph minors. II. Algorithmic aspects of tree-width, Journal of Algorithms, vol.7, issue.3, pp.309-322, 1986.
DOI : 10.1016/0196-6774(86)90023-4
URL : https://doi.org/10.1006/jctb.1996.0059

D. J. Rose, A graph theoretic study of the numerical solution of sparse positive denite systems of linear equations, Graph Theory and Computing, pp.183-217, 1973.

D. Sabin and E. Freuder, Contradicting conventional wisdom in constraint satisfaction, Proceedings of ECAI, pp.125-129, 1994.
DOI : 10.1007/3-540-58601-6_86

D. Sabin and E. Freuder, Understanding and improving the MAC algorithm, Proceedings of CP, pp.167-181, 1997.
DOI : 10.1007/BFb0017438
URL : http://4c.ucc.ie/web/upload/publications/inProc/sabin97understanding.ps

R. Tarjan and M. Yannakakis, Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs, SIAM Journal on Computing, vol.13, issue.3, pp.566-579, 1984.
DOI : 10.1137/0213035

T. Walsh, Search in a small world, Proceedings of IJCAI, pp.1172-1177, 1999.