The space complexity of approximating the frequency moments

Noga Alon; Yossi Matias; Mario Szegedy

doi:10.1145/237814.237823

The space complexity of approximating the frequency moments

Noga Alon, Yossi Matias, Mario Szegedy

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

600 Scopus citations

Abstract

The frequency moments of a sequence containing m_i elements of type i, for 1 ≤ i ≤ n, are the numbers F_k = Σⁿ _i=1 m^k_i. We consider the space complexity of randomized algorithms that approximate the numbers F_k, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F₀, F₁ and F₂ can be approximated in logarithmic space, whereas the approximation of F_k for k ≥ 6 requires n^Ω(1) space. Applications to data bases are mentioned as well.

Original language	English (US)
Title of host publication	Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996
Publisher	Association for Computing Machinery
Pages	20-29
Number of pages	10
ISBN (Electronic)	0897917855
DOIs	https://doi.org/10.1145/237814.237823
State	Published - Jul 1 1996
Externally published	Yes
Event	28th Annual ACM Symposium on Theory of Computing, STOC 1996 - Philadelphia, United States Duration: May 22 1996 → May 24 1996

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F129452
ISSN (Print)	0737-8017

Other

Other	28th Annual ACM Symposium on Theory of Computing, STOC 1996
Country/Territory	United States
City	Philadelphia
Period	5/22/96 → 5/24/96

All Science Journal Classification (ASJC) codes

Software

Access to Document

10.1145/237814.237823

Cite this

@inproceedings{97d6433adce842878ba6ae8805d36c30,

title = "The space complexity of approximating the frequency moments",

abstract = "The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = Σn i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires nΩ(1) space. Applications to data bases are mentioned as well.",

author = "Noga Alon and Yossi Matias and Mario Szegedy",

note = "Publisher Copyright: {\textcopyright} 1996 ACM.; 28th Annual ACM Symposium on Theory of Computing, STOC 1996 ; Conference date: 22-05-1996 Through 24-05-1996",

year = "1996",

month = jul,

day = "1",

doi = "10.1145/237814.237823",

language = "English (US)",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "20--29",

booktitle = "Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996",

}

Alon, N, Matias, Y & Szegedy, M 1996, The space complexity of approximating the frequency moments. in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F129452, Association for Computing Machinery, pp. 20-29, 28th Annual ACM Symposium on Theory of Computing, STOC 1996, Philadelphia, United States, 5/22/96. https://doi.org/10.1145/237814.237823

The space complexity of approximating the frequency moments. / Alon, Noga; Matias, Yossi; Szegedy, Mario.
Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996. Association for Computing Machinery, 1996. p. 20-29 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129452).

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

TY - GEN

T1 - The space complexity of approximating the frequency moments

AU - Alon, Noga

AU - Matias, Yossi

AU - Szegedy, Mario

PY - 1996/7/1

Y1 - 1996/7/1

N2 - The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = Σn i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires nΩ(1) space. Applications to data bases are mentioned as well.

AB - The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = Σn i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires nΩ(1) space. Applications to data bases are mentioned as well.

UR - http://www.scopus.com/inward/record.url?scp=0029719644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029719644&partnerID=8YFLogxK

U2 - 10.1145/237814.237823

DO - 10.1145/237814.237823

M3 - Conference contribution

AN - SCOPUS:0029719644

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 20

EP - 29

BT - Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996

PB - Association for Computing Machinery

T2 - 28th Annual ACM Symposium on Theory of Computing, STOC 1996

Y2 - 22 May 1996 through 24 May 1996

ER -

The space complexity of approximating the frequency moments

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this