Skip to main content
SpringerLink
Log in
Book cover

Complexity of Constraints pp 156–195Cite as

Uniform Constraint Satisfaction Problems and Database Theory

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5250))

Abstract

It is well-known that there is a close similarity between constraint satisfaction and conjunctive query evaluation. This paper explains this relationship and describes structural query decomposition methods that can equally be used to decompose CSP instances. In particular, we explain how “islands of tractability” can be achieved by decomposing the query on a database, or, equivalently, the scopes of a constraint satisfaction problem. We focus on advanced decomposition methods such as hypertree decompositions, which are hypergraph-based and subsume earlier graph-based decomposition methods. We also discuss generalizations thereof, such as weighted hypertree decompositions, and subedge-based decompositions. Finally, we report on an interesting new type of structural tractability results that, rather than explicitly computing problem decompositions, use algorithms that are guaranteed to find a correct solution in polynomial time if a decomposition exists.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)

    MATH  Google Scholar 

  2. Abiteboul, S., Duschka, O.M.: Complexity of Answering Queries Using Materialized Views. In: Proc. of the PODS 1998, Seattle, Washington, pp. 254–263 (1998)

    Google Scholar 

  3. Adler, I.: Marshals, Monotone Marshals, and Hypertree-Width. Journal of Graph Theory 47(4), 275–296 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Adler, I., Gottlob, G., Grohe, M.: Hypertree-Width and Related Hypergraph Invariants. In: Proc. of EuroComb 2005, Berlin (2005)

    Google Scholar 

  5. Atserias, A., Bulatov, A., Dalmau, V.: On the Power of k-Consistency. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 279–290. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Journal of the ACM 30(3), 479–513 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Van Benthem, J.: Dynamic Bits and Pieces. ILLC Research Report, University of Amsterdam (1997)

    Google Scholar 

  8. Bernstein, P.A., Goodman, N.: The power of natural semijoins. SIAM Journal on Computing 10(4), 751–771 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bodlaender, H.L., Fomin, F.V.: Tree decompositions with small cost. Discrete Applied Mathematics 145(2), 143–154 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cai, J., Chakaravarthy, V.T., Kaushik, R., Naughton, J.F.: On the Complexity of Join Predicates. In: Proc. of PODS 2001 (2001)

    Google Scholar 

  11. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the ACM 26, 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chandra, A.K., Merlin, P.M.: Optimal Implementation of Conjunctive Queries in relational Databases. In: Proc. of STOC 1977, pp. 77–90 (1977)

    Google Scholar 

  13. Chen, H., Dalmau, V.: Beyond hypertree width: Decomposition methods without decompositions. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 167–181. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Chekuri, C., Rajaraman, A.: Conjunctive query containment revisited. Theoretical Computer Science 239(2), 211–229 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Chung, F., Frank, P., Graham, R., Shearer, J.: Some intersection theorems for ordered sets and graphs. Journal of Combinatorial Theory, Series A 43, 23–37 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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, Edinburgh, UK, pp. 72–77 (2005)

    Google Scholar 

  17. Cohen, D.A., Jeavons, P.G., Gyssens, M.: A unified theory of structural tractability for constraint satisfaction problems. Journal of Computer and System Sciences 74(5), 721–743 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Cook, W., Seymour, P.: Tour merging via branch-decomposition. INFORMS Journal on Computing 15(3), 233–248 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dalmau, V., Kolaitis, P.G., Vardi, M.Y.: Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 310–326. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Dechter, R.: Constraint networks. In: Shapiro, S.C. (ed.) Encyclopedia of Artificial Intelligence, 2nd edn., vol. 1, pp. 276–285. Wiley, Chichester (1992)

    Google Scholar 

  21. Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)

    MATH  Google Scholar 

  22. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  23. Fagin, R., Mendelzon, A.O., Ullman, J.D.: A simplified universal relation assumption and its properties. ACM Transactions on Database Systems 7(3), 343–360 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fagin, R., Kolaitis, P.G., Popa, L.: Data exchange: getting to the core. ACM Trans. Database Syst. 30(1), 174–210 (2005)

    Article  MATH  Google Scholar 

  25. Feder, T., Vardi, M.Y.: The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM Journal of Computing 28, 57–104 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  26. Flum, J., Frick, M., Grohe, M.: Query evaluation via tree-decompositions. Journal of the ACM 49(6), 716–752 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  27. Freuder, E.C.: A sufficient condition for backtrack-bounded search. Journal of ACM 32(4), 755–761 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  28. Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM 48(6), 1184–1206 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  30. Garcia-Molina, H., Ullman, J., Widom, J.: Database system implementation. Prentice Hall, Englewood Cliffs (2000)

    Google Scholar 

  31. Ghionna, L., Granata, L., Greco, G., Scarcello, F.: Hypertree Decompositions for Query Optimization. In: Proc. of ICDE 2007, pp. 36–45 (2007)

    Google Scholar 

  32. Goodman, N., Shmueli, O.: Tree queries: a simple class of relational queries. ACM Transactions on Database Systems 7(4), 653–6773 (1982)

    Article  MATH  Google Scholar 

  33. Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. Journal of Computer and System Sciences 64(3), 579–627 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Gottlob, G., Leone, N., Scarcello, F.: A comparison of structural CSP decomposition methods. Artificial Intelligence 124(2), 243–282 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  35. Gottlob, G., Leone, N., Scarcello, F.: Advanced parallel algorithms for processing acyclic conjunctive queries, rules, and constraints. In: Proceedings of the 2000 Conference on Software Engineering and Knowledge Engineering (SEKE 2000), Chicago, pp. 167–176 (2000)

    Google Scholar 

  36. 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)

    Chapter  Google Scholar 

  37. Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. Journal of the ACM 48(3), 431–498 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  38. Gottlob, G., Leone, N., Scarcello, F.: Computing LOGCFL Certificates. Theoretical Computer Science 270(1-2), 761–777 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  39. Gottlob, G., Leone, N., Scarcello, F.: Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width. Journal of Computer and System Sciences 66(4), 775–808 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gottlob, G., Grohe, M., Musliu, N., Samer, M., Scarcello, F.: Hypertree decompositions: Structure, algorithms, and applications. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 1–15. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  41. Gottlob, G., Miklos, Z., Schwentick, T.: Generalized hypertree decompositions: NP-Hardness and Tractable Variants. In: Proc. of PODS 2007, pp. 13–22 (2007)

    Google Scholar 

  42. Gottlob, G., Samer, M.: A Backtracking-Based Algorithm for Computing Hypertree-Decompositions. arXiv:cs/0701083 (2007)

    Google Scholar 

  43. Grädel, E.: On the Restraining Power of Guards. Journal of Symbolic Logic 64, 1719–1742 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  44. Greibach, S.H.: The Hardest Context-Free Language. SIAM Journal on Computing 2(4), 304–310 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  45. Greco, G., Scarcello, F.: Non-Binary Constraints and Optimal Dual-Graph Representations. In: Proc. of IJCAI 2003, pp. 227–232 (2003)

    Google Scholar 

  46. Grohe, M.: The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side. Journal of the ACM 54(1) (2007)

    Google Scholar 

  47. Grohe, M., Marx, D.: Constraint solving via fractional edge covers. In: Proc. of SODA 2006, Miami, Florida, USA, pp. 289–298 (2006)

    Google Scholar 

  48. Grohe, M., Schwentick, T., Segoufin, L.: When is the evaluation of conjunctive queries tractable? In: Proc. of STOC 2001, Heraklion, Crete, Greece, pp. 657–666 (2001)

    Google Scholar 

  49. Gyssens, M., Jeavons, P.G., Cohen, D.A.: Decomposing constraint satisfaction problems using database techniques. Journal of Algorithms 66, 57–89 (1994)

    MathSciNet  MATH  Google Scholar 

  50. Harvey, P., Ghose, A.: Reducing Redundancy in the Hypertree Decomposition Scheme. In: Proc. of 5th IEEE International Conference on Tools with Artificial Intelligence, pp. 474–481 (2003)

    Google Scholar 

  51. Ioannidis, Y.E.: Query Optimization. The Computer Science and Engineering Handbook, pp. 1038–1057 (1997)

    Google Scholar 

  52. Ioannidis, Y.E.: The History of Histograms (abridged). In: Proc. of VLDB 2003, Berlin, Germany, pp. 19–30 (2003)

    Google Scholar 

  53. Johnson, D.S.: A Catalog of Complexity Classes. In: Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, pp. 67–161 (1990)

    Google Scholar 

  54. Kolaitis, P.G.: Constraint Satisfaction, Databases, and Logic. In: Proc. of IJCAI 2003, Acapulco, Mexico, pp. 1587–1595 (2003)

    Google Scholar 

  55. Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences 61(2), 302–332 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  56. Korimort, T.: Constraint Satisfaction Problems – Heuristic Decomposition. Ph.D thesis, Vienna University of Technology (April 2003)

    Google Scholar 

  57. Kun, G.: Constraints, MMSNP and expander relational structures (2007) ArXiv.org, http://www.citebase.org/abstract?id=oai:arXiv.org:0706.1701

  58. Maier, D.: The Theory of Relational Databases. Computer Science Press (1986)

    Google Scholar 

  59. McMahan, B.: Bucket eliminiation and hypertree decompositions. Implementation report, Institute of Information Systems (DBAI), TU Vienna (2004)

    Google Scholar 

  60. Musliu, N.: Tabu Search for Generalized Hypertree Decompositions. In: Proc. of MIC 2007 (2007)

    Google Scholar 

  61. Reingold, O.: Undirected ST-connectivity in log-space. In: Proc. of STOC 2005, Baltimore, MD, USA, pp. 376–385 (2005)

    Google Scholar 

  62. McMahan, B.J., Pan, G., Porter, P., Vardi, M.Y.: Projection Pushing Revisited. In: Bertino, E., Christodoulakis, S., Plexousakis, D., Christophides, V., Koubarakis, M., Böhm, K., Ferrari, E. (eds.) EDBT 2004. LNCS, vol. 2992, pp. 441–458. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  63. Papadimitriou, C.H., Yannakakis, M.: On the complexity of database queries. In: Proc. of PODS 1997, Tucson, Arizona, pp. 12–19 (1997)

    Google Scholar 

  64. Pearson, J., Jeavons, P.G.: A Survey of Tractable Constraint Satisfaction Problems, CSD-TR-97-15, Royal Holloway, Univ. of London (1997)

    Google Scholar 

  65. Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree width. Journal of Algorithms 7, 309–322 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  66. Ruzzo, W.L.: Tree-size bounded alternation. Journal of Cumputer and System Sciences 21, 218–235 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  67. Saccà, D.: Closures of database hypergraphs. Journal of the ACM 32(4), 774–803 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  68. Samer, M.: Hypertree-decomposition via Branch-decomposition. In: Proceeding of IJCAI 2005, pp. 1535–1536 (2005)

    Google Scholar 

  69. Scarcello, F.: The Hypertree Decompositions HomePage (2002), http://www.deis.unical.it/scarcello/Hypertrees/ , http://www.dbai.tuwien.ac.at/proj/hypertree/ maintained by N. Musliu

  70. Scarcello, F., Greco, G., Leone, N.: Weighted Hypertree Decompositions and Optimal Query Plans. In: Proc. of PODS 2004, pp. 210–221 (2004)

    Google Scholar 

  71. 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)

    Article  MathSciNet  MATH  Google Scholar 

  72. Seidel, R.: A new method for solving constraint satisfaction problems. In: Proc. of IJCAI 1981 (1981)

    Google Scholar 

  73. Subbarayan, S., Andersen, H.R.: Backtracking Procedures for Hypertree, HyperSpread and Connected Hypertree Decomposition of CSPs. In: Proc. of IJCAI 2007, pp. 180–185 (2007)

    Google Scholar 

  74. Skyum, S., Valiant, L.G.: A complexity theory based on Boolean algebra. Journal of the ACM 32, 484–502 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  75. Sudborough, I.H.: Time and Tape Bounded Auxiliary Pushdown Automata. In: Gruska, J. (ed.) MFCS 1977. LNCS, vol. 53, pp. 493–503. Springer, Heidelberg (1977)

    Chapter  Google Scholar 

  76. Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13(3), 566–579 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  77. Ullman, J.D.: Principles of Database and Knowledge Base Systems. Computer Science Press (1989)

    Google Scholar 

  78. Vardi, M.: Complexity of relational query languages. In: Proc. of STOC 1982, San Francisco, California, United States, pp. 137–146 (1982)

    Google Scholar 

  79. Vardi, M.: Constraint Satisfaction and Database Theory. In: Tutorial at the 19th ACM Symposium on Principles of Database Systems, PODS 2000 (2000)

    Google Scholar 

  80. Wilschut, A.N., Flokstra, J., Apers, P.M.G.: Parallel evaluation of multi-join queries. In: Proceedings of SIGMOD 1995, San Jose, CA, USA, pp. 115–126 (1995)

    Google Scholar 

  81. Yannakakis, M.: Algorithms for acyclic database schemes. In: Proc. of VLDB 1981, Cannes, France, pp. 82–94 (1981)

    Google Scholar 

  82. Yu, C.T., Özsoyoğlu, M.Z.: On determining tree-query membership of a distributed query. Infor. 22(3), 261–282 (1984)

    MATH  Google Scholar 

  83. Yu, C.T., Özsoyoğlu, M.Z., Lam, K.: Optimization of Distributed Tree Queries. Journal of Computer and System Sciences 29(3), 409–445 (1984)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DEIS, Università della Calabria, Italy

    Francesco Scarcello

  2. Computing Laboratory, University of Oxford, UK

    Georg Gottlob

  3. Dipartimento di Matematica, Università della Calabria, Italy

    Gianluigi Greco

Authors
  1. Francesco Scarcello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georg Gottlob
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gianluigi Greco
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LIF (CNRS UMR 6166), Aix-Marseille Université, 163 avenue de Luminy, F-13288, Marseille, France

    Nadia Creignou

  2. IBM Almaden Research Center, Computer Science Principles and Methodologies, and Computer Science Department, University of California, Santa Cruz, USA

    Phokion G. Kolaitis

  3. Institut für Theoretische Informatik, Leibniz, Universität Hannover, Appelstr. 4, 30167, Hannover, Germany

    Heribert Vollmer

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Scarcello, F., Gottlob, G., Greco, G. (2008). Uniform Constraint Satisfaction Problems and Database Theory. In: Creignou, N., Kolaitis, P.G., Vollmer, H. (eds) Complexity of Constraints. Lecture Notes in Computer Science, vol 5250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92800-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-92800-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92799-0

  • Online ISBN: 978-3-540-92800-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation