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The Maximum Size of Dynamic Data Structures

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vitter, Jeffrey Scott Kenyon-Mathieu, Claire M.
Copyright Year	1991
Abstract	This paper develops two probabilistic methods that allow the analysis of the maximum data structure size encountered during a sequence of insertions and deletions in data structures such as priority queues, dictionaries, linear lists, and symbol tables, and in sweepline structures for geometry and Very-Large-Scale-Integration (VLSI) applications. The notion of the maximum is basic to issues of resource preallocation. The methods here are applied to combinatorial models of file histories and probabilistic models, as well as to a non-Markovian process (algorithm) for processing sweepline information in an efficient way, called hashing with lazy deletion (HwLD). Expressions are derived for the expected maximum data structure size that are asymptotically exact, that is, correct up to lower-order terms; in several cases of interest the expected value of the maximum size is asymptotically equal to the maximum expected size. This solves several open problems, including longstanding questions in queueing theory. Both of these approaches are robust and rely upon novel applications of techniques from the analysis of algorithms. At a high level, the first method isolates the primary contribution to the maximum and bounds the lesser effects. In the second technique the continuous-time probabilistic model is related to its discrete analogthe maximum slot occupancy in hashing.
Starting Page	807
Ending Page	823
Page Count	17
File Format	PDF
ISSN	00975397
DOI	10.1137/0220050
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Markov process file histories queueing theory analysis of algorithms VLSI hashing computational geometry lazy deletion sweepline lists priority queues symbol tables maximum data structures occupancy distribution dictionaries
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Maximum Size of a Dynamic Data Structure: Hashing with Lazy Deletion Revisited

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