Hypertree Decompositions: Structure, Algorithms, and Applications

  • Georg Gottlob
  • Martin Grohe
  • Nysret Musliu
  • Marko Samer
  • Francesco Scarcello
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)


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.


Constraint Satisfaction Problem Winning Strategy Chordal Graph Primal Graph Conjunctive Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adler, I.: Marshals, monotone marshals, and hypertree width. Journal of Graph Theory 47, 275–296 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Adler, I., Gottlob, G., Grohe, M.: Hypertree-width and related hypergraph invariants. Manuscript, submitted for publication, available from the authorsGoogle Scholar
  3. 3.
    Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational databases. In: Proc. STOC 1977, pp. 77–90 (1977)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Dechter, R.: Constraint networks. In: Encyclopedia of Artificial Intelligence, 2nd edn., pp. 276–285. Wiley & Sons, Chichester (1992)Google Scholar
  6. 6.
    Dechter, R., Pearl, J.: Network-based heuristics for constraint satisfaction problems. Artificial Intelligence 34(1), 1–38 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38(3), 353–366 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  9. 9.
    Freuder, E.C.: A sufficient condition for backtrack bounded search. Journal of the ACM 32(4), 755–761 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    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) Google Scholar
  11. 11.
    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)CrossRefMathSciNetGoogle Scholar
  12. 12.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    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) zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    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) zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Gottlob, G., Pichler, R.: Hypergraphs in model checking: Acyclicity and hypertree-width versus clique-width. Siam Journal of Computing 33(2), 351–378 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Gyssens, M., Jeavons, P.G., Cohen, D.A.: Decomposing constraint satisfaction problems using database techniques. Artificial Intelligence 66, 57–89 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Gyssens, M., Paredaens, J.: A decomposition methodology for cyclic databases. In: Advances in Database Theory, vol. 2, pp. 85–122 (1984)Google Scholar
  20. 20.
    Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences (JCSS) 61, 302–332 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Korimort, T.: Constraint satisfaction problems – Heuristic decomposition. PhD thesis, Vienna University of Technology (April 2003)Google Scholar
  22. 22.
    Maier, D.: The theory of relational databases. Computer Science Press, Rockville (1986)Google Scholar
  23. 23.
    McMahan, B.: Bucket eliminiation and hypertree decompositions. Implementation report, Institute of Information Systems (DBAI), TU Vienna (2004)Google Scholar
  24. 24.
    Pearson, J., Jeavons, P.G.: A survey of tractable constraint satisfaction problems. Technical report CSD-TR-97-15, Royal Halloway University of London (1997)Google Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    Robertson, N., Seymour, P.D.: Graph minors. X. Obstructions to tree-decomposition. Journal of Combinatorial Theory, Series B 52, 153–190 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Ruzzo, W.L.: Tree-size bounded alternation. Journal of Computer and System Sciences (JCSS) 21(2), 218–235 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Samer, M.: Hypertree-decomposition via branch-decomposition. In: Proc. IJCAI 2005, pp. 1535–1536 (2005)Google Scholar
  29. 29.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Yannakakis, M.: Algorithms for acyclic database schemes. In: Proc. VLDB 1981, pp. 82–94 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Georg Gottlob
    • 1
  • Martin Grohe
    • 2
  • Nysret Musliu
    • 1
  • Marko Samer
    • 1
  • Francesco Scarcello
    • 3
  1. 1.Institut für InformationssystemeTU WienViennaAustria
  2. 2.Institut für InformatikHumboldt-UniversitätBerlinGermany
  3. 3.D.E.I.S.University of CalabriaRende (CS)Italy

Personalised recommendations