TY - JOUR
T1 - The space complexity of approximating the frequency moments
AU - Alon, Noga
AU - Matias, Yossi
AU - Szegedy, Mario
N1 - Funding Information:
- Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel. Research supported in part by a USA-Israel BSF grant and by the Fund for Basic Research administered by the Israel Academy of Sciences.
PY - 1999/2
Y1 - 1999/2
N2 - The frequency moments of a sequence containing mi elements of type i, 1≤i≤n, are the numbers Fk=Σni=1mki. 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, 1≤i≤n, are the numbers Fk=Σni=1mki. 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 - https://www.scopus.com/pages/publications/0033077324
U2 - 10.1006/jcss.1997.1545
DO - 10.1006/jcss.1997.1545
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AN - SCOPUS:0033077324
SN - 0022-0000
VL - 58
SP - 137
EP - 147
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 1
ER -