Threshold and Symmetric Functions over Bitmaps

TL;DR

This paper explores extending bitmap indexes to efficiently support symmetric Boolean queries like threshold functions, demonstrating competitive algorithms that produce bitmap results suitable for further processing.

Contribution

It introduces algorithms for symmetric Boolean queries over bitmaps, showing they are competitive with state-of-the-art methods and produce reusable bitmap results.

Findings

Bitmap algorithms are competitive with existing solutions.

Results are bitmap outputs that can be further processed.

Extended applicability of bitmap indexes to advanced queries.

Abstract

Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the application of bitmap indexes to more advanced queries. We want to extend the applicability of bitmap indexes. As a starting point, we consider symmetric Boolean queries (e.g., threshold functions). For example, we might consider stores as sets of products, and ask for products that are on sale in 2 to 10 stores. Such symmetric Boolean queries generalize intersection, union, and T-occurrence queries. It may not be immediately obvious to an engineer how to use bitmap indexes for symmetric Boolean queries. Yet, maybe surprisingly, we find that the best of our bitmap-based algorithms are competitive with the state-of-the-art algorithms for important special cases (e.g., MergeOpt, MergeSkip, DivideSkip, ScanCount). Moreover, unlike the competing algorithms, the result of our computation is again a bitmap which can be further processed within a bitmap index. We review algorithmic design issues such as the aggregation of many compressed bitmaps. We conclude with a discussion on other advanced queries that bitmap indexes might be able to support efficiently.