Colliding stacks: A large deviations analysis

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher‐order asymptotics follow from WKB expansions.

Original languageEnglish (US)
Pages (from-to)379-420
Number of pages42
JournalRandom Structures & Algorithms
Volume2
Issue number4
DOIs
StatePublished - 1991

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Hamiltonians
Large Deviations
Markov processes
Mechanics
Data storage equipment
Hamiltonian Formulation
Classical Mechanics
Deletion
Insertion
Markov chain
Collision
Likely

Keywords

  • dynamic data structures
  • large deviations
  • Markov chains
  • storage allocation

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Cite this

Colliding stacks : A large deviations analysis. / Maier, Robert S.

In: Random Structures & Algorithms, Vol. 2, No. 4, 1991, p. 379-420.

Research output: Contribution to journalArticle

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