The asymptotic evolution of data structures

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The evolution of certain pointer-based implementations of dictionaries, linear lists and priority queues is studied. Under the assumption of equiprobability of histories, i.e., of paths through the internal state space of the implementation, the n → ∞ asymptotics of the space and time costs of a sequence of n supported operations are computed. For list implementations the mean integrated spatial cost is asymptotically proportional to n2, and its standard deviation to n3/2. For d-heap implementations of priority queues the mean integrated space cost grows only as n2/√log n, i.e. more slowly than the worst-case integrated cost. The standard deviation grows as n3/2. These asymptotics reflect the convergence as n → ∞ of the normalized structure sizes to datatype-dependent deterministic functions of time, as earlier discovered by Louchard. This phenomenon is clarified with the aid of large deviation theory, and path integral techniques.

Original languageEnglish (US)
Title of host publicationAdvances in Computing and Information – ICCI 1990 - International Conference on Computing and Information, Proceedings
EditorsWaldemar W. Koczkodaj, Selim G. Akl, Frantisek Fiala
PublisherSpringer-Verlag
Pages13-23
Number of pages11
ISBN (Print)9783540535041
DOIs
StatePublished - 1990
EventInternational Conference on Computing and Information, ICCI 1990 - Niagara Falls, Canada
Duration: May 23 1990May 26 1990

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume468 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherInternational Conference on Computing and Information, ICCI 1990
CountryCanada
CityNiagara Falls
Period5/23/905/26/90

Keywords

  • Dynamic data structures
  • Expected costs
  • Large deviations
  • Stochastic modelling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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