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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
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

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 Sorting Priority queues 

Notes

Acknowledgments

We thank Oleksii Starov for suggesting this problem to us.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Michael A. Bender
    • 1
  • Rezaul Chowdhury
    • 1
  • Alexander Conway
    • 2
  • Martín Farach-Colton
    • 2
  • Pramod Ganapathi
    • 1
  • Rob Johnson
    • 1
  • Samuel McCauley
    • 1
  • Bertrand Simon
    • 3
  • Shikha Singh
    • 1
  1. 1.Stony Brook UniversityStony BrookUSA
  2. 2.Rutgers UniversityPiscatawayUSA
  3. 3.LIP, ENS de LyonLyonFrance

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