Parallel Mapper

TL;DR

This paper introduces a parallel algorithm for constructing Mapper, a topological data analysis tool, demonstrating its correctness and efficiency through performance experiments on multiple processors.

Contribution

We develop and validate the first provably correct parallel algorithm for Mapper construction, improving scalability and performance in topological data analysis.

Findings

Parallel Mapper algorithm is correct and scalable.

Performance experiments show significant efficiency gains.

Our approach outperforms sequential implementations.

Abstract

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method.