Space Lower Bounds for Itemset Frequency Sketches
Abstract
Given a database, computing the fraction of rows that contain a query itemset or determining whether this fraction is above some threshold are fundamental operations in data mining. A uniform sample of rows is a good sketch of the database in the sense that all sufficiently frequent itemsets and their approximate frequencies are recoverable from the sample, and the sketch size is independent of the number of rows in the original database. For many seemingly similar problems there are better sketching algorithms than uniform sampling. In this paper we show that for itemset frequency sketching this is not the case. That is, we prove that there exist classes of databases for which uniform sampling is a space optimal sketch for approximate itemset frequency analysis, up to constant or iteratedlogarithmic factors.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.3740
 Bibcode:
 2014arXiv1407.3740L
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Minor edits for clarity, and added some discussion of subsequent work. To appear in PODS 2016