Query Answering and Containment for Regular Path Queries under Distortions

  • Gösta Grahne
  • Alex Thomo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2942)


We give a general framework for approximate query processing in semistructured databases. We focus on regular path queries, which are the integral part of most of the query languages for semistructured databases. To enable approximations, we allow the regular path queries to be distorted. The distortions are expressed in the system by using weighted regular expressions, which correspond to weighted regular transducers. After defining the notion of weighted approximate answers we show how to compute them in order of their proximity to the query. In the new approximate setting, query containment has to be redefined in order to take into account the quantitative proximity information in the query answers. For this, we define approximate containment, and its variants k-containment and reliable containment. Then, we give an optimal algorithm for deciding the k-containment. Regarding the reliable approximate containment, we show that it is polynomial time equivalent to the notorious limitedness problem in distance automata.


Regular Expression Graph Database Query Answer Query Answering Semistructured Data 
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. [ABS99]
    Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and Xml. Morgan Kaufmann Pulishers, San Francisco (1999)Google Scholar
  2. [AHU74]
    Aho, A., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)zbMATHGoogle Scholar
  3. [C+99]
    Calvanese, D., Giacomo, G., Lenzerini, M., Vardi, M.Y.: Rewriting of Regular Expressions and Regular Path Queries. In: Proc. PODS 1999, pp. 194–204 (1999)Google Scholar
  4. [C+00]
    Calvanese, D., Giacomo, G., Lenzerini, M., Vardi, M.Y.: View-Based Query Processing and Constraint Satisfaction. In: Proc. LICS 2000, pp. 361–371 (2000)Google Scholar
  5. [GT00]
    Grahne, G., Thomo, A.: An Optimization Technique for Answering Regular Path Queries. In: Suciu, D., Vossen, G. (eds.) WebDB 2000. LNCS, vol. 1997, pp. 99–104. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. [GT01]
    Grahne, G., Thomo, A.: Algebraic rewritings for optimizing regular path queries. In: Van den Bussche, J., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 303–315. Springer, Heidelberg (2000)Google Scholar
  7. [Has82]
    Hashiguchi, K.: Limitedness Theorem on Finite Automata with Distance Functions. J. Comp. Syst. Sci. 24(2), 233–244 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Has90]
    Hashiguchi, K.: Improved Limitedness Theorems on Finite Automata with Distance Functions. Theoretical Computer Science 72(1), 27–38 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  9. [Has00]
    Hashiguchi, K.: New upper bounds to the limitedness of distance automata. Theoretical Computer Science 233(1-2), 19–32 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [HU79]
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  11. [HRS76]
    Hunt III, H.B., Rosenkrantz, D.J., Szymanski, T.G.: On the Equivalence, Containment, and Covering Problems for the Regular and Context-Free Languages. J. Comp. Syst. Sci. 12(2), 222–268 (1976)zbMATHMathSciNetCrossRefGoogle Scholar
  12. [Kru83]
    Kruskal, J.: An Overview of Sequence Comparison. In: Sankoff, D., Kruskal, J. (eds.) Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, pp. 1–44. Addison-Wesley, Reading (1983)Google Scholar
  13. [JMM95]
    Jagadish, H.V., Mendelzon, A.O., Milo, T.: Similarity-Based Queries. In: Proc. PODS 1995, pp. 36–45 (1995)Google Scholar
  14. [Leu91]
    Leung, H.: Limitedness Theorem on Finite Automata with Distance Functions: An Algebraic Proof. Theoretical Computer Science 81(1), 137–145 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  15. [MW95]
    Mendelzon, A.O., Wood, P.T.: Finding Regular Simple Paths in Graph Databases. SIAM J. Comp. 24(6), 1235–1258 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  16. [MMM97]
    Mendelzon, A.O., Mihaila, G.A., Milo, T.: Querying the World Wide Web. Int. J. Dig. Lib. 1(1), 57–67 (1997)Google Scholar
  17. [Pin98]
    Pin, J.E.: Tropical Semirings. In: Gunawardena, J. (ed.) Idempotency, pp. 50–69. Cambridge University Press, Cambridge (1998)CrossRefGoogle Scholar
  18. [Sim94]
    Simon, I.: On Semigroups of Matrices over the Tropical Semiring. Informatique Theorique et Applications 28(3-4), 277–294 (1994)zbMATHGoogle Scholar
  19. [WF74]
    Wagner, R.A., Fischer, M.J.: The String-to-String Correction Problem. J. ACM 21(1), 168–173 (1974)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Gösta Grahne
    • 1
  • Alex Thomo
    • 2
  1. 1.Concordia UniversityMontrealCanada
  2. 2.Suffolk UniversityBostonUSA

Personalised recommendations