Worst Case Optimal Union-Intersection Expression Evaluation

  • Ehsan Chiniforooshan
  • Arash Farzan
  • Mehdi Mirzazadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets. Given the expression and the sizes of the sets, we are interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume no set is repeated in the expression. We show a lower bound on this problem and present an algorithm that matches the lower bound asymptotically.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. In: Proceedings of the seventh international conference on World Wide Web, vol. 7, pp. 107–117. Elsevier Science Publishers B. V, Amsterdam (1998)Google Scholar
  2. 2.
    Brown, M.R., Tarjan, R.E.: A fast merging algorithm. J. ACM 26(2), 211–226 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Brown, M.R., Tarjan, R.E.: Design and analysis of a data structure for representing sorted lists. SIAM Journal of Computing 9(3), 594–614 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Demaine, E.D., Lopez-Ortiz, A., Munro, J.I.: Adaptive set intersections, unions, and differences. In: Proc. of Eleventh ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 743–752 (2000)Google Scholar
  5. 5.
    Hwang, F.K., Lin, S.: A simple algorithm for merging two disjoint linearly ordered sets. SIAM Journal on Computing 1(1), 31–39 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lee, G., Park, M., Won, H.: Using syntactic information in handling natural language quries for extended boolean retrieval model. In: Proceedings of the 4th international workshop on information retrieval with Asian languages (1999)Google Scholar
  7. 7.
    Mauldin, M.I.Lycos Inc., and PA Pittsburgh. Lycos: design choices in an internet search service. IEEE Expert, 12(1):8–11, 1997.Google Scholar
  8. 8.
    Mirzazadeh, M.: Adaptive comparison-based algorithms for evaluating set queries. Master’s thesis, School of Computer Science, University of Waterloo (2004)Google Scholar
  9. 9.
    Pugh, W.: A skip list cookbook. Technical Report CS-TR-2286.1, University of Maryland (1990)Google Scholar
  10. 10.
    Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill, Inc., New York (1990)zbMATHGoogle Scholar
  11. 11.
    Witten, I.H., Bell, T.C., Moffat, A.: Managing Gigabytes: Compressing and Indexing Documents and Images. John Wiley & Sons, Inc., Chichester (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ehsan Chiniforooshan
    • 1
  • Arash Farzan
    • 1
  • Mehdi Mirzazadeh
    • 1
  1. 1.School of Computer ScienceUniversity of Waterloo 

Personalised recommendations