Exponential structures for efficient cache-oblivious algorithms

Michael A. Bender, Richard Cole, Rajeev Raman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present cache-oblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider are searching, partial persistence and planar point location. On a hierarchical memory where data is transferred in blocks of size B, some of the results we achieve are: - We give a linear-space data structure for dynamic searching that supports searches and updates in optimal O(logB N) worst-case I/Os, eliminating amortization from the result of Bender, Demaine, and Farach-Colton (FOCS '00).We also consider finger searches and updates and batched searches. - We support partially-persistent operations on an ordered set, namely, we allow searches in any previous version of the set and updates to the latest version of the set (an update creates a new version of the set). All operations take an optimal O(logB(m+N)) amortized I/Os, whereN is the size of the version being searched/updated, and m is the number of versions. - We solve the planar point location problem in linear space, taking optimal O(logB N) I/Os for point location queries, where N is the number of line segments specifying the partition of the plane. The pre-processing requires O((N/B) logM/B N) I/Os, where M is the size of the 'inner' memory.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
Pages195-207
Number of pages13
Volume2380 LNCS
StatePublished - 2002
Event29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 - Malaga, Spain
Duration: Jul 8 2002Jul 13 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2380 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other29th International Colloquium on Automata, Languages, and Programming, ICALP 2002
CountrySpain
CityMalaga
Period7/8/027/13/02

Fingerprint

Cache
Point Location
Data structures
Update
Data storage equipment
Data Structures
Linear Space
Ordered Set
Location Problem
Line segment
Persistence
Preprocessing
Partition
Query
Processing
Partial

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bender, M. A., Cole, R., & Raman, R. (2002). Exponential structures for efficient cache-oblivious algorithms. In Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings (Vol. 2380 LNCS, pp. 195-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2380 LNCS).

Exponential structures for efficient cache-oblivious algorithms. / Bender, Michael A.; Cole, Richard; Raman, Rajeev.

Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. Vol. 2380 LNCS 2002. p. 195-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2380 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bender, MA, Cole, R & Raman, R 2002, Exponential structures for efficient cache-oblivious algorithms. in Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. vol. 2380 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2380 LNCS, pp. 195-207, 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002, Malaga, Spain, 7/8/02.
Bender MA, Cole R, Raman R. Exponential structures for efficient cache-oblivious algorithms. In Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. Vol. 2380 LNCS. 2002. p. 195-207. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Bender, Michael A. ; Cole, Richard ; Raman, Rajeev. / Exponential structures for efficient cache-oblivious algorithms. Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. Vol. 2380 LNCS 2002. pp. 195-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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