## Sketching and Streaming High-Dimensional Vectors (2011)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Nelson11sketchingand,

author = {Jelani Nelson and Erik D. Demaine},

title = {Sketching and Streaming High-Dimensional Vectors},

year = {2011}

}

### OpenURL

### Abstract

A sketch of a dataset is a small-space data structure supporting some prespecified set of queries (and possibly updates) while consuming space substantially sublinear in the space required to actually store all the data. Furthermore, it is often desirable, or required by the application, that the sketch itself be computable by a small-space algorithm given just one pass over the data, a so-called streaming algorithm. Sketching and streaming have found numerous applications in network traffic monitoring, data mining, trend detection, sensor networks, and databases. In this thesis, I describe several new contributions in the area of sketching and streaming algorithms. • The first space-optimal streaming algorithm for the distinct elements problem. Our algorithm also achieves O(1) update and reporting times. • A streaming algorithm for Hamming norm estimation in the turnstile model which achieves the best known space complexity.

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Citation Context ...re discussion of empirical entropy estimation in data streams in the context of network anomaly detection. The first algorithms for approximating entropy in the streaming model are due to Guha et al. =-=[60]-=-; they achieved O((ε −2 +log d) log 2 d) space in the insertion-only model, assuming that the stream is randomly ordered. Chakrabarti, Do Ba and Muthukrishnan [26] then gave an algorithm for worst-cas... |

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