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DOI: 10.4230/LIPIcs.ICALP.2018.25
URN: urn:nbn:de:0030-drops-90294
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9029/
Braverman, Vladimir ; Viola, Emanuele ; Woodruff, David P. ; Yang, Lin F.
Revisiting Frequency Moment Estimation in Random Order Streams
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Abstract
We revisit one of the classic problems in the data stream literature, namely, that of estimating the frequency moments F_p for 0 < p < 2 of an underlying n-dimensional vector presented as a sequence of additive updates in a stream. It is well-known that using p-stable distributions one can approximate any of these moments up to a multiplicative (1+epsilon)-factor using O(epsilon^{-2} log n) bits of space, and this space bound is optimal up to a constant factor in the turnstile streaming model. We show that surprisingly, if one instead considers the popular random-order model of insertion-only streams, in which the updates to the underlying vector arrive in a random order, then one can beat this space bound and achieve O~(epsilon^{-2} + log n) bits of space, where the O~ hides poly(log(1/epsilon) + log log n) factors. If epsilon^{-2} ~~ log n, this represents a roughly quadratic improvement in the space achievable in turnstile streams. Our algorithm is in fact deterministic, and we show our space bound is optimal up to poly(log(1/epsilon) + log log n) factors for deterministic algorithms in the random order model. We also obtain a similar improvement in space for p = 2 whenever F_2 >~ log n * F_1.
BibTeX - Entry
@InProceedings{braverman_et_al:LIPIcs:2018:9029,
author = {Vladimir Braverman and Emanuele Viola and David P. Woodruff and Lin F. Yang},
title = {{Revisiting Frequency Moment Estimation in Random Order Streams}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {25:1--25:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9029},
URN = {urn:nbn:de:0030-drops-90294},
doi = {10.4230/LIPIcs.ICALP.2018.25},
annote = {Keywords: Data Stream, Frequency Moments, Random Order, Space Complexity, Insertion Only Stream}
}
| Keywords: | Data Stream, Frequency Moments, Random Order, Space Complexity, Insertion Only Stream | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
