Range Counting Coresets for Uncertain Data

TL;DR

This paper develops new coreset constructions for range counting queries on uncertain data, enabling efficient approximate query answering by summarizing the data with small, representative subsets.

Contribution

It introduces novel coreset methods for three types of uncertain range counting queries, with improved bounds using discrepancy techniques and random sampling.

Findings

Coresets enable efficient approximate range counting on uncertain data.

Discrepancy-based methods improve coreset size bounds.

Random sampling provides a simple alternative for coreset construction.

Abstract

We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximation-size tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancy-based approaches on axis-aligned range queries.