### 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(log_{B} 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(log_{B}(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(log_{B} 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) log_{M/B} N) I/Os, where M is the size of the 'inner' memory.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings |

Pages | 195-207 |

Number of pages | 13 |

Volume | 2380 LNCS |

State | Published - 2002 |

Event | 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 - Malaga, Spain Duration: Jul 8 2002 → Jul 13 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2380 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 |
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Country | Spain |

City | Malaga |

Period | 7/8/02 → 7/13/02 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Exponential structures for efficient cache-oblivious algorithms

AU - Bender, Michael A.

AU - Cole, Richard

AU - Raman, Rajeev

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84869180878&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869180878&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540438645

SN - 9783540438649

VL - 2380 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 195

EP - 207

BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings

ER -