Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs

TL;DR

This paper introduces a novel single-pass algorithm, Propagate and Pair, for pairing critical points in Reeb graphs, improving efficiency in topological data analysis applications.

Contribution

The paper presents a new single-pass algorithm for critical point pairing in Reeb graphs, advancing the computational methods in topological data analysis.

Findings

The single-pass Propagate and Pair algorithm is more efficient than multipass methods.

The approach enhances the computation of persistence diagrams from Reeb graphs.

Experimental results demonstrate improved performance in large data sets.

Abstract

With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself. Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. Although the body of work addressing the efficient calculation of Reeb graphs is large, the literature on pairing is limited. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.