An approximate Lp-difference algorithm for massive data streams

TL;DR: In this paper, the Indifference Σ i |a i - b i | p for any rational-valued p E (0,2), with comparable efficiency and error, is presented.

Abstract: Several recent papers have shown how to approximate the difference Σ i |a i - b i | or Σ |a i - b i | 2 between two functions, when the function values a i and b i are given in a data stream, and their order is chosen by an adversary. These algorithms use little space (much less than would be needed to store the entire stream) and little time to process each item in the stream and give approximations with small relative error. Using different techniques, we show how to approximate the Indifference Σ i |a i - b i | p for any rational-valued p E (0,2], with comparable efficiency and error. We also show how to approximate Σ i |a i - b i | p for larger values of p but with a worse error guarantee. These results can be used to assess the difference between two chronologically or physically separated massive data sets, making one quick pass over each data set, without buffering the data or requiring the data source to pause.