Article

Biased dictionaries with fast insert/deletes

Authors:

S. Cenk Sahinalp,

Jonathan Sharp,

Rakesh SinhaAuthors Info & Claims

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

Pages 483 - 491

https://doi.org/10.1145/380752.380843

Published: 06 July 2001 Publication History

Abstract

A dictionary data structure supports efficient search, insert, and delete operations on n keys from a totally ordered universe. Red-black trees, 2-3 trees, AVL trees, skip lists and other classic data structures facilitate O(logn) time search, insert and deletes, matching the information theoretic lower bound when access probabilities are uniform i.i.d. If access probabilities are non-uniform but still i.i.d., there are other weighted data structures such as D-trees, biased search trees, splay trees and treaps which can achieve optimality.

In many applications, however, the source of nonuniformity in access probabilities is locality of reference: examples include memory, cache, disk and buffer management and emerging applications in internetwork traffic management. In such applications, the access probability of any given key is not i.i.d., but decreases with idle time since the last access to the key.

It is possible to adjust the weighted dictionaries to achieve optimal search time even under time dependent distributions; however insert/delete times will be suboptimal at O(logn). In this paper, we present a lazy updating scheme which can be applied to weighted dictionaries to improve their amortized insert/delete performance when access probabilities decrease with time; optimality of search time is preserved. More speci%cally, let r(k) be the number of distinct keys accessed since the last access to key k- that is r(k) is the move-to-front rank of k. Let rmax(k) be the maximum rank of k during its lifetime.

Then our lazy update scheme enables the abovementioned data structures to perform search in O(log r(k)) time and insert/delete in O(log rmax(k)) time. We illustrate our lazy update scheme in the context of a new Biased Skip List data structure and show that our bounds are optimal.

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Cited By

Bose PDouïeb KLangerman STeng S(2008)Dynamic optimality for skip lists and B-treesProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347203(1106-1114)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347203
Ciriani VFerragina PLuccio FMuthukrishnan S(2007)A data structure for a sequence of string accesses in external memoryACM Transactions on Algorithms10.1145/1186810.11868163:1(1-23)Online publication date: 2-Feb-2007
https://dl.acm.org/doi/10.1145/1186810.1186816
Bagchi ABuchsbaum AGoodrich M(2002)Biased Skip ListsAlgorithms and Computation10.1007/3-540-36136-7_1(1-13)Online publication date: 8-Nov-2002
https://doi.org/10.1007/3-540-36136-7_1

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Biased dictionaries with fast insert/deletes

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cover image ACM Conferences

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

July 2001

755 pages

ISBN:1581133499

DOI:10.1145/380752

Copyright © 2001 ACM.

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Published: 06 July 2001

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Cited By

Bose PDouïeb KLangerman STeng S(2008)Dynamic optimality for skip lists and B-treesProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347203(1106-1114)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347203
Ciriani VFerragina PLuccio FMuthukrishnan S(2007)A data structure for a sequence of string accesses in external memoryACM Transactions on Algorithms10.1145/1186810.11868163:1(1-23)Online publication date: 2-Feb-2007
https://dl.acm.org/doi/10.1145/1186810.1186816
Bagchi ABuchsbaum AGoodrich M(2002)Biased Skip ListsAlgorithms and Computation10.1007/3-540-36136-7_1(1-13)Online publication date: 8-Nov-2002
https://doi.org/10.1007/3-540-36136-7_1

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