A Unified Approach to Linear Probing Hashing with Buckets

We give a unified analysis of linear probing hashing with a general bucket size. We use both a combinatorial approach, giving exact formulas for generating functions, and a probabilistic approach, giving simple derivations of asymptotic results. Both approaches complement nicely, and give a good ins...

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Veröffentlicht in:Algorithmica Jg. 75; H. 4; S. 724 - 781
Hauptverfasser: Janson, Svante, Viola, Alfredo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2016
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Analytic combinatorics
Buckets
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Generating functions
Hashing
Linear probing
Mathematics of Computing
Theory of Computation
Linear probing
Generating functions
Hashing
60W40
Analytic combinatorics
Buckets
68P10
68P20
ISSN:0178-4617, 1432-0541, 1432-0541
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Beschreibung
Zusammenfassung:We give a unified analysis of linear probing hashing with a general bucket size. We use both a combinatorial approach, giving exact formulas for generating functions, and a probabilistic approach, giving simple derivations of asymptotic results. Both approaches complement nicely, and give a good insight in the relation between linear probing and random walks. A key methodological contribution, at the core of Analytic Combinatorics, is the use of the symbolic method (based on q -calculus) to directly derive the generating functions to analyze.
ISSN:0178-4617
1432-0541
1432-0541
DOI:10.1007/s00453-015-0111-x