Methods in the analysis of algorithms : Evaluations of a recursive partitioning process

  • Philippe Flajolet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)


We show how the analysis of a large number of algorithms used for sorting, searching, retrieving multidimensional data, accessing external files, factoring polynomials, implementing communication protocols... reduce to the study of a simple recursive partitioning process. We present systematic methods for obtaining from the structural definitions of characteristic parameters of the process corresponding average values in either exact or asymptotic form through the use of generating functions.


Binary Sequence Generate Polynomial Partial Match Binary Search Tree Partition Tree 
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.


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  1. [AHU83]
    A. Aho, J. Hopcroft, J. Ullman: "Data Structures and Algorithms", Addison Wesley, Reading (1983).Google Scholar
  2. [FFH82]
    G. Fayolle, P. Flajolet, M. Hofri: "A Functional Equation Arising in the Analysis of a Protocol for a Multiaccess Broadcast Channel", INRIA Research Report no 131, 36 pages.Google Scholar
  3. [FS81]
    P. Flajolet, J-M. Steyaert: "A Complexity Calculus for Classes of Recursive Search Programs Over Tree Structures" in 22nd IEEE FOCS Symp., Nashville (1982), pp. 386–393.Google Scholar
  4. [FNPS79]
    R. Fagin, J. Nievergelt, N. Pippenger, R. Strong: "Extendible Hahing-A Fast Access Method for Dynamic Files", ACM TODS, 4 (1979), pp. 315–344.CrossRefGoogle Scholar
  5. [FSa82]
    P. Flajolet, N. Saheb: "Digital Search Trees and the Complexity of Generating an Exponentially Distributed Variate", in CAAP 82, Lecture Notes in Comp. Sc. (to appear).Google Scholar
  6. [FSo82]
    P. Flajolet, D. Sotteau: "A Recursive Partitioning Process of Computer Science", in IInd World Conference on Mathematics at the Service of Man, Las Palmas (1982), pp. 25–30.Google Scholar
  7. [FSt82]
    P. Flajolet, J-M. Steyaert: "A Branching Process Arising in Dynamic Hashing Trie Searching and Polynomial Factorization", ICALP 82, Lectures Notes in Comp. Sc. 140, (1982), pp. 239–251.Google Scholar
  8. [FPu83]
    P. Flajolet, C. Puech: "Tree Structures for Partial Match Retrieval of Multidimensional Data", submitted for publication (1983).Google Scholar
  9. [He78]
    P. Henrici: "Applied and Computational Complex Analysis", vol. 2, J. Wiley New York (1978).Google Scholar
  10. [Kn71]
    D.E. Knuth: "Mathematical Analysis of Algorithms", in IFIP Congress 1971, Ljubljana.Google Scholar
  11. [Kn73]
    D.E. Knuth: "The Art of Computer Programming", vol. 3, Addison Wesley, Reading (1973).Google Scholar
  12. [La78]
    P.A. Larson: "Dynamic Hashing", BIT, 18(1978), pp. 184–201.Google Scholar
  13. [Li78]
    W. Litwin: "Virtual Hashing: A Dynamically Changing Hashing", in Proc. VLDB Conf., Berlin (1978), pp. 517–523.Google Scholar
  14. [Ma80]
    J.L. Massey: "Collision Resolution Algorithms and Random Access Communication", in Multi-User Communication Systems, CISM Lectures no 265, G. Longo Ed., Springer Verlag (1980).Google Scholar
  15. [NHS81]
    J. Nievergelt, H. Hinterberger, K. Sevick: "The Grid File: An Adaptable Symmetric Multikey File Structure", ETH Report 46 (1981).Google Scholar
  16. [Ri76]
    R.L. Rivest: "Partial Match Retrieval Algorithms", SIAM J. Comp. 51 (1976), pp. 19–50.Google Scholar
  17. [Re83]
    M. Regnier: "Evaluation des Performances du Hachage Dynamique", Thesis, University of Paris-Orsay (1983).Google Scholar
  18. [Se82]
    R. Sedgewick: "Mathematical Analysis of Combinatorial Algorithms", in Probability Theory and Computer Science, G. Louchard, G. Latouche Ed., Academic Press, New York (1982).Google Scholar
  19. [Se83]
    R. Sedgewick: "Algorithms", Addison-Wesley, Reading (1983).Google Scholar
  20. [TP78]
    L. Trabb Pardo: "Set Representation and Set Intersection", Stanford Univ. Report CS-78-681 (1978).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Philippe Flajolet
    • 1
  1. 1.INRIA, RocquencourtLe ChesnayFrance

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