Finding two-tree-factor elements of tableau-defined monoids in time O(n3)

  • Alois P. Heinz
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)


We consider the problem of finding elements in tableau-defined monoids. The solution of this problem is important to the minimization of restricted relational database queries. Although the problem has been shown to be NP-complete in general, many polynomial-time algorithms have been proposed for some subclasses of the general problem. The contribution of this paper is a new algorithm that finds elements with two-tree-factors in time O(n3). The number of elements that can be found in polynomial time is significantly increased by our algorithm as compared with the algorithms known so far.

Key words

relational database relational algebra query optimization tableaux 


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  1. [1]
    M. Abramowitz and I. A. Stegun, editors. Handbook of mathematical functions. Dover Publications, Inc., New York, 1965.Google Scholar
  2. [2]
    A. V. Aho, Y. Sagiv, and J. D. Ullman. Effizient optimization of a class of relational expressions. ACM Trans. Database Syst., 4(4):435–454, December 1979.Google Scholar
  3. [3]
    A. V. Aho, Y. Sagiv, and J. D. Ullman. Equivalences among relational expressions. SIAM J. Comput., 8(2):218–246, May 1979.Google Scholar
  4. [4]
    B. Harris and L. Schoenfeld. The number of idempotent elements in symmetric semigroups. Journal of Combinatorial Theory, 3(2):122–135, September 1967.Google Scholar
  5. [5]
    A. P. Heinz. Optimization of Relational Algebra Queries. Master's thesis, Rheinisch-Westfälische Technische Hochschule Aachen, March 1984. in German.Google Scholar
  6. [6]
    A. P. Heinz and G. Vossen. Quadratic-time optimization of SPJ-expressions including inequality selections by tableaux. Fundamenta Informaticae VIII, 8(3–4):397–414, 1985.Google Scholar
  7. [7]
    Y. Sagiv. Quadratic algorithms for minimizing joins in restricted relational expressions. SIAM J. Comput., 12(2):316–328, May 1983.Google Scholar
  8. [8]
    Y. Sagiv and M. Yannakakis. Equivalences among relational expressions with the union and difference operators. J. ACM, 27(4):633–655, October 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alois P. Heinz
    • 1
  1. 1.Institut für InformatikUniversität FreiburgFreiburg

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