The I/O complexity of computing prime tables

Michael A. Bender; Rezaul Chowdhury; Alexander Conway; Martín Farach-Colton; Pramod Ganapathi; Rob Johnson; Samuel McCauley; Bertrand Simon; Shikha Singh

doi:10.1007/978-3-662-49529-2_15

The I/O complexity of computing prime tables

Michael A. Bender, Rezaul Chowdhury, Alexander Conway, Martín Farach-Colton, Pramod Ganapathi, Rob Johnson, Samuel McCauley, Bertrand Simon, Shikha Singh

SAS - Computer Science

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

Abstract

We revisit classical sieves for computing primes and analyze their performance in the external-memory model. Most prior sieves are analyzed in the RAM model, where the focus is on minimizing both the total number of operations and the size of the working set. The hope is that if the working set fits in RAM, then the sieve will have good I/O performance, though such an outcome is by no means guaranteed by a small working-set size. We analyze our algorithms directly in terms of I/Os and operations. In the external-memory model, permutation can be the most expensive aspect of sieving, in contrast to the RAM model, where permutations are trivial. We show how to implement classical sieves so that they have both good I/O performance and good RAM performance, even when the problem size N becomes huge—even superpolynomially larger than RAM. Towards this goal, we give two I/O-efficient priority queues that are optimized for the operations incurred by these sieves.

Original language	English (US)
Title of host publication	LATIN 2016
Subtitle of host publication	Theoretical Informatics - 12th Latin American Symposium, Proceedings
Editors	Gonzalo Navarro, Evangelos Kranakis, Edgar Chávez
Publisher	Springer Verlag
Pages	192-206
Number of pages	15
ISBN (Print)	9783662495285
DOIs	https://doi.org/10.1007/978-3-662-49529-2_15
State	Published - 2016
Event	12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico Duration: Apr 11 2016 → Apr 15 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9644
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	12th Latin American Symposium on Theoretical Informatics, LATIN 2016
Country	Mexico
City	Ensenada
Period	4/11/16 → 4/15/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Keywords

External-memory algorithms
Prime tables
Priority queues
Sorting

Access to Document

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Bender, M. A., Chowdhury, R., Conway, A., Farach-Colton, M., Ganapathi, P., Johnson, R., McCauley, S., Simon, B., & Singh, S. (2016). The I/O complexity of computing prime tables. In G. Navarro, E. Kranakis, & E. Chávez (Eds.), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings (pp. 192-206). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_15

Bender, Michael A. ; Chowdhury, Rezaul ; Conway, Alexander ; Farach-Colton, Martín ; Ganapathi, Pramod ; Johnson, Rob ; McCauley, Samuel ; Simon, Bertrand ; Singh, Shikha. / The I/O complexity of computing prime tables. LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. editor / Gonzalo Navarro ; Evangelos Kranakis ; Edgar Chávez. Springer Verlag, 2016. pp. 192-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "The I/O complexity of computing prime tables",

abstract = "We revisit classical sieves for computing primes and analyze their performance in the external-memory model. Most prior sieves are analyzed in the RAM model, where the focus is on minimizing both the total number of operations and the size of the working set. The hope is that if the working set fits in RAM, then the sieve will have good I/O performance, though such an outcome is by no means guaranteed by a small working-set size. We analyze our algorithms directly in terms of I/Os and operations. In the external-memory model, permutation can be the most expensive aspect of sieving, in contrast to the RAM model, where permutations are trivial. We show how to implement classical sieves so that they have both good I/O performance and good RAM performance, even when the problem size N becomes huge—even superpolynomially larger than RAM. Towards this goal, we give two I/O-efficient priority queues that are optimized for the operations incurred by these sieves.",

keywords = "External-memory algorithms, Prime tables, Priority queues, Sorting",

author = "Bender, {Michael A.} and Rezaul Chowdhury and Alexander Conway and Mart{\'i}n Farach-Colton and Pramod Ganapathi and Rob Johnson and Samuel McCauley and Bertrand Simon and Shikha Singh",

note = "Funding Information: This research was supported by NSF grants CCF 1217708, IIS 1247726, IIS 1251137, CNS 1408695, CCF 1439084, CNS-1408782, IIS-1247750, and Sandia National Laboratories Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2016.; 12th Latin American Symposium on Theoretical Informatics, LATIN 2016 ; Conference date: 11-04-2016 Through 15-04-2016",

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doi = "10.1007/978-3-662-49529-2_15",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Bender, MA, Chowdhury, R, Conway, A, Farach-Colton, M, Ganapathi, P, Johnson, R, McCauley, S, Simon, B & Singh, S 2016, The I/O complexity of computing prime tables. in G Navarro, E Kranakis & E Chávez (eds), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9644, Springer Verlag, pp. 192-206, 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, Ensenada, Mexico, 4/11/16. https://doi.org/10.1007/978-3-662-49529-2_15

The I/O complexity of computing prime tables. / Bender, Michael A.; Chowdhury, Rezaul; Conway, Alexander; Farach-Colton, Martín; Ganapathi, Pramod; Johnson, Rob; McCauley, Samuel; Simon, Bertrand; Singh, Shikha.

LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. ed. / Gonzalo Navarro; Evangelos Kranakis; Edgar Chávez. Springer Verlag, 2016. p. 192-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644).

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

TY - GEN

T1 - The I/O complexity of computing prime tables

AU - Bender, Michael A.

AU - Chowdhury, Rezaul

AU - Conway, Alexander

AU - Farach-Colton, Martín

AU - Ganapathi, Pramod

AU - Johnson, Rob

AU - McCauley, Samuel

AU - Simon, Bertrand

AU - Singh, Shikha

N1 - Funding Information: This research was supported by NSF grants CCF 1217708, IIS 1247726, IIS 1251137, CNS 1408695, CCF 1439084, CNS-1408782, IIS-1247750, and Sandia National Laboratories Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2016.

PY - 2016

Y1 - 2016

N2 - We revisit classical sieves for computing primes and analyze their performance in the external-memory model. Most prior sieves are analyzed in the RAM model, where the focus is on minimizing both the total number of operations and the size of the working set. The hope is that if the working set fits in RAM, then the sieve will have good I/O performance, though such an outcome is by no means guaranteed by a small working-set size. We analyze our algorithms directly in terms of I/Os and operations. In the external-memory model, permutation can be the most expensive aspect of sieving, in contrast to the RAM model, where permutations are trivial. We show how to implement classical sieves so that they have both good I/O performance and good RAM performance, even when the problem size N becomes huge—even superpolynomially larger than RAM. Towards this goal, we give two I/O-efficient priority queues that are optimized for the operations incurred by these sieves.

AB - We revisit classical sieves for computing primes and analyze their performance in the external-memory model. Most prior sieves are analyzed in the RAM model, where the focus is on minimizing both the total number of operations and the size of the working set. The hope is that if the working set fits in RAM, then the sieve will have good I/O performance, though such an outcome is by no means guaranteed by a small working-set size. We analyze our algorithms directly in terms of I/Os and operations. In the external-memory model, permutation can be the most expensive aspect of sieving, in contrast to the RAM model, where permutations are trivial. We show how to implement classical sieves so that they have both good I/O performance and good RAM performance, even when the problem size N becomes huge—even superpolynomially larger than RAM. Towards this goal, we give two I/O-efficient priority queues that are optimized for the operations incurred by these sieves.

KW - External-memory algorithms

KW - Prime tables

KW - Priority queues

KW - Sorting

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U2 - 10.1007/978-3-662-49529-2_15

DO - 10.1007/978-3-662-49529-2_15

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SN - 9783662495285

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

SP - 192

EP - 206

BT - LATIN 2016

A2 - Navarro, Gonzalo

A2 - Kranakis, Evangelos

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PB - Springer Verlag

T2 - 12th Latin American Symposium on Theoretical Informatics, LATIN 2016

Y2 - 11 April 2016 through 15 April 2016

ER -

Bender MA, Chowdhury R, Conway A, Farach-Colton M, Ganapathi P, Johnson R et al. The I/O complexity of computing prime tables. In Navarro G, Kranakis E, Chávez E, editors, LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Springer Verlag. 2016. p. 192-206. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-49529-2_15

The I/O complexity of computing prime tables

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All Science Journal Classification (ASJC) codes

Keywords

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