Rapid Sampling for Visualizations with Ordering Guarantees

TL;DR

This paper introduces fast sampling algorithms for visualizations that guarantee the preservation of ordering properties, enabling rapid approximate visualizations with minimal samples and high accuracy.

Contribution

The paper presents novel sampling algorithms that are provably optimal for preserving ordering in visualizations, significantly reducing sampling time compared to traditional methods.

Findings

Algorithms are theoretically optimal in sample complexity.

Practically, they produce correct orderings with far fewer samples.

They outperform conventional sampling schemes in speed and accuracy.

Abstract

Visualizations are frequently used as a means to understand trends and gather insights from datasets, but often take a long time to generate. In this paper, we focus on the problem of rapidly generating approximate visualizations while preserving crucial visual proper- ties of interest to analysts. Our primary focus will be on sampling algorithms that preserve the visual property of ordering; our techniques will also apply to some other visual properties. For instance, our algorithms can be used to generate an approximate visualization of a bar chart very rapidly, where the comparisons between any two bars are correct. We formally show that our sampling algorithms are generally applicable and provably optimal in theory, in that they do not take more samples than necessary to generate the visualizations with ordering guarantees. They also work well in practice, correctly ordering output groups while taking orders of magnitude fewer samples and much less time than conventional sampling schemes.