Abstract
We review the concepts of hypertree decomposition and hypertree width from a graph theoretical perspective and report on a number of recent results related to these concepts. We also show – as a new result – that computing hypertree decompositions is fixed-parameter intractable.
This paper was supported by the Austrian Science Fund (FWF) project: Nr. P17222-N04, Complementary Approaches to Constraint Satisfaction. Correspondence to: Georg Gottlob, Institut für Informationssysteme, TU Wien, Favoritenstr. 9-11/184-2, A-1040 Wien, Austria, E-mail: gottlob@acm.org.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adler, I.: Marshals, monotone marshals, and hypertree width. Journal of Graph Theory 47, 275–296 (2004)
Adler, I., Gottlob, G., Grohe, M.: Hypertree-width and related hypergraph invariants. Manuscript, submitted for publication, available from the authors
Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational databases. In: Proc. STOC 1977, pp. 77–90 (1977)
Cohen, D.A., Jeavons, P.G., Gyssens, M.: A unified theory of structural tractability for constraint satisfaction and spread cut decomposition. In: Proc. IJCAI 2005, pp. 72–77 (2005)
Dechter, R.: Constraint networks. In: Encyclopedia of Artificial Intelligence, 2nd edn., pp. 276–285. Wiley & Sons, Chichester (1992)
Dechter, R., Pearl, J.: Network-based heuristics for constraint satisfaction problems. Artificial Intelligence 34(1), 1–38 (1987)
Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38(3), 353–366 (1989)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Freuder, E.C.: A sufficient condition for backtrack bounded search. Journal of the ACM 32(4), 755–761 (1985)
Gottlob, G., Greco, G., Scarcello, F.: Pure Nash equilibria: Hard and easy games. Journal of Artificial Intelligence Research, JAIR (2005) (To appear); Preliminary version In: Proc. TARK 2003 (2003)
Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. Journal of the ACM 48(3), 431–498 (2001); Preliminary version in: Proc. FOCS 1998 (1998)
Gottlob, G., Leone, N., Scarcello, F.: Computing LOGCFL certificates. Theoretical Computer Science 270(1-2), 761–777 (2002); Preliminary version In: Proc. ICALP 1999 (1999)
Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. Journal of Computer and System Sciences (JCSS) 64(3), 579–627 (2002); Preliminary version In: Proc. PODS 1999, (1999)
Gottlob, G., Leone, N., Scarcello, F.: On tractable queries and constraints. In: Bench-Capon, T.J.M., Soda, G., Tjoa, A.M. (eds.) DEXA 1999. LNCS, vol. 1677, pp. 1–15. Springer, Heidelberg (1999)
Gottlob, G., Leone, N., Scarcello, F.: A comparison of structural CSP decomposition methods. Artificial Intelligence 124(2), 243–282 (2000); Preliminary version In: Proc. IJCAI 1999 (1999)
Gottlob, G., Leone, N., Scarcello, F.: Robbers, marshals, and guards: Game-theoretic and logical characterizations of hypertree width. In: Proc. PODS 2001, pp. 195–206 (2001)
Gottlob, G., Pichler, R.: Hypergraphs in model checking: Acyclicity and hypertree-width versus clique-width. Siam Journal of Computing 33(2), 351–378 (2004)
Gyssens, M., Jeavons, P.G., Cohen, D.A.: Decomposing constraint satisfaction problems using database techniques. Artificial Intelligence 66, 57–89 (1994)
Gyssens, M., Paredaens, J.: A decomposition methodology for cyclic databases. In: Advances in Database Theory, vol. 2, pp. 85–122 (1984)
Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences (JCSS) 61, 302–332 (2000)
Korimort, T.: Constraint satisfaction problems – Heuristic decomposition. PhD thesis, Vienna University of Technology (April 2003)
Maier, D.: The theory of relational databases. Computer Science Press, Rockville (1986)
McMahan, B.: Bucket eliminiation and hypertree decompositions. Implementation report, Institute of Information Systems (DBAI), TU Vienna (2004)
Pearson, J., Jeavons, P.G.: A survey of tractable constraint satisfaction problems. Technical report CSD-TR-97-15, Royal Halloway University of London (1997)
Reed, B.: Tree width and tangles: A new connectivity measure and some applications. In: Surveys in Combinatorics. LNCS, vol. 241, pp. 87–162. Cambridge University Press, Cambridge (1997)
Robertson, N., Seymour, P.D.: Graph minors. X. Obstructions to tree-decomposition. Journal of Combinatorial Theory, Series B 52, 153–190 (1991)
Ruzzo, W.L.: Tree-size bounded alternation. Journal of Computer and System Sciences (JCSS) 21(2), 218–235 (1980)
Samer, M.: Hypertree-decomposition via branch-decomposition. In: Proc. IJCAI 2005, pp. 1535–1536 (2005)
Seymour, P.D., Thomas, R.: Graph searching and a min-max theorem for tree-width. Journal of Combinatorial Theory, Series B 58, 22–33 (1993)
Yannakakis, M.: Algorithms for acyclic database schemes. In: Proc. VLDB 1981, pp. 82–94 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gottlob, G., Grohe, M., Musliu, N., Samer, M., Scarcello, F. (2005). Hypertree Decompositions: Structure, Algorithms, and Applications. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_1
Download citation
DOI: https://doi.org/10.1007/11604686_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
Online ISBN: 978-3-540-31468-4
eBook Packages: Computer ScienceComputer Science (R0)