An efficient implicit data structure for path testing and searching in rooted trees and forests

  • Giorgio Gambosi
  • Marco Protasi
  • Maurizio Talamo
Geometric Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 405)


In this paper, an implicit data structure is presented which makes it possible to represent a tree-structured partial order in such a way to efficiently perform operations of path testing and searching among elements of the ground set of the poset. The data structure makes it possible to represent the order relation by referring only to internal nodes of the tree and by associating to each element of the ground set a pair of integer values derived from specific linear extensions of the partial order.

CR Classification

E1 (Data structures) F2 (Analysis of algorithms and problem complexity) 


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5. References

  1. [AMM84]
    H. Alt,K. Melhorn,J.I. Munro "Partial match retrieval in implicit data structures" Inf. Proc; Lett., 19, 2, (1984).Google Scholar
  2. [ASSS86]
    M.D. Atkinson,J.R. Sack,N. Santoro,T. Strohotte "Min-Max heaps and generalized priority queues" Comm.A.C.M., 29,10, (1986).Google Scholar
  3. [BFMUW86]
    A.Borodin,F.E.Fich,F.Meyer auf der Heide,E.Upfal, A.Widgerson "A tradeoff between search and update time for the implicit dictionary problem" Proc. 13th ICALP Conf., Lect. Not. in Comp. Sci., 226, Springer Verlag, (1986).Google Scholar
  4. [F83]
    G.N. Frederickson "Implicit data structures for the dictionary problem" J. Ass. Comp. Mach., 30,1, (1983).Google Scholar
  5. [GNT89]
    G.Gambosi,E.Nardelli,M.Talamo "A pointer-free data structure for merging heaps and min-max heaps" Proc.16th ICALP Conf., Lect. Not. in Comp. Sci., 372, Springer Verlag, (1989).Google Scholar
  6. [M86]
    J.I. Munro "An implicit data structure supporting insertion, deletion and search in O(log2n) time" J. Comp. Syst. Sci., 33, 1, (1986).CrossRefGoogle Scholar
  7. [MS80]
    J.I. Munro, H. Suwanda "Implicit data structures for fast search and update" J. Comp. Syst. Sci., 21, 2, (1980).Google Scholar
  8. [SS85]
    J.R.Sack, T.Strothotte "An algorithm for merging heaps" Act. Inf., 22, (1985).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Giorgio Gambosi
    • 1
  • Marco Protasi
    • 2
  • Maurizio Talamo
    • 3
    • 1
  1. 1.Istituto di analisi dei sistemi ed informatica del CNRRomaItaly
  2. 2.Dipartimento di MatematicaII Università di Roma "Tor Vergata"RomaItaly
  3. 3.Dipartimento di MatematicaUniversità dell'AquilaL'AquilaItaly

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