A path integral approach to data structure evolution

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A probabilistic analysis is presented of certain pointer-based implementations of dictionaries, linear lists, and priority queues; in particular, simple list and d-heap implementations. Under the assumption of equiprobability of histories, i.e., of paths through the internal state space of the implementation, it is shown that the integrated space and time costs of a sequence of n supported operations converge as n → ∞ to Gaussian random variables. For list implementations the mean integrated spatial costs grow asymptotically as n2, and the standard deviations of the costs as n 3 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 n 3 2. These asymptotic growth rates 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 path integrals. Path integral techniques, drawn from physics, greatly facilitate the computation of the cost asymptotics. This is their first application to the analysis of dynamic data structures.

Original languageEnglish (US)
Pages (from-to)232-260
Number of pages29
JournalJournal of Complexity
Volume7
Issue number3
DOIs
StatePublished - 1991

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Curvilinear integral
Data structures
Data Structures
Costs
Priority Queue
Heap
Standard deviation
Dynamic Data Structures
Probabilistic Analysis
Glossaries
Random variables
State Space
Physics
Random variable
Internal
Converge
Path
Dependent

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Analysis
  • Computational Mathematics

Cite this

A path integral approach to data structure evolution. / Maier, Robert S.

In: Journal of Complexity, Vol. 7, No. 3, 1991, p. 232-260.

Research output: Contribution to journalArticle

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