1-Pass Relative-Error L_p-Sampling with Applications

Tight bounds for Lp samplers, finding duplicates in streams, and related problems

“…In the past decade, several sampling techniques have been proposed and studied for the data stream model [3,11,5,10,22,1]. In this work, we study Lp-samplers, a new variant of space efficient samplers for data streams that was introduced by Monemizadeh and Woodruff in [22].…”

“…In the past decade, several sampling techniques have been proposed and studied for the data stream model [3,11,5,10,22,1]. In this work, we study Lp-samplers, a new variant of space efficient samplers for data streams that was introduced by Monemizadeh and Woodruff in [22]. Roughly speaking, given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x ∈ R n , an Lp-sampler processes the stream and outputs a sample coordinate of x where the i-th coordinate is picked with probability proportional to |xi| p .…”

“…Roughly speaking, given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x ∈ R n , an Lp-sampler processes the stream and outputs a sample coordinate of x where the i-th coordinate is picked with probability proportional to |xi| p . In [22], it was observed that Lp-samplers lead to alternative algorithms for many known streaming problems, including heavy hitters and frequency moment estimation. Here in this paper, we focus on a specific application, namely finding duplicates in long streams; although our Lp samplers work and often give better space performance for all applications listed in [22].…”

“…In [22], it was observed that Lp-samplers lead to alternative algorithms for many known streaming problems, including heavy hitters and frequency moment estimation. Here in this paper, we focus on a specific application, namely finding duplicates in long streams; although our Lp samplers work and often give better space performance for all applications listed in [22]. We refer the reader to [22] and [1] for further applications of Lp-samplers.…”

“…Here in this paper, we focus on a specific application, namely finding duplicates in long streams; although our Lp samplers work and often give better space performance for all applications listed in [22]. We refer the reader to [22] and [1] for further applications of Lp-samplers.…”