Distributed Discrete Morse Sandwich: Efficient Computation of Persistence Diagrams for Massive Scalar Data

2025-05-27

AI Summary

To address the challenge of efficiently computing persistence diagrams for large-scale 3D scalar fields using discrete Morse–Sandwich (DMS) algorithms in distributed-memory environments, this paper introduces the first end-to-end distributed DMS framework. Methodologically, we design a self-correcting distributed pairing algorithm, reconstruct a distributed data structure enabling cross-node gradient propagation, and integrate a computation token mechanism with dedicated communication threads to overlap communication and computation under an MPI-plus-multithreading hybrid programming model. Our contribution is the first scalable multi-node DMS implementation, breaking prior scalability bottlenecks and enabling persistent homology analysis on 3D scalar fields with up to 10 billion cells. Experiments demonstrate excellent strong and weak scaling up to 512 cores; our method achieves an average 8× speedup over DIPHA; and it computes the full persistence diagram for a 6-billion-vertex dataset in just 174 seconds.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Large-scale security measurements

Abstract

The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The"Discrete Morse Sandwich"(DMS) method has been reported to be the most efficient algorithm for computing persistence diagrams of 3D scalar fields on a single node, using shared-memory parallelism. In this work, we extend DMS to distributed-memory parallelism for the efficient and scalable computation of persistence diagrams for massive datasets across multiple compute nodes. On the one hand, we can leverage the embarrassingly parallel procedure of the first and most time-consuming step of DMS (namely the discrete gradient computation). On the other hand, the efficient distributed computations of the subsequent DMS steps are much more challenging. To address this, we have extensively revised the DMS routines by contributing a new self-correcting distributed pairing algorithm, redesigning key data structures and introducing computation tokens to coordinate distributed computations. We have also introduced a dedicated communication thread to overlap communication and computation. Detailed performance analyses show the scalability of our hybrid MPI+thread approach for strong and weak scaling using up to 16 nodes of 32 cores (512 cores total). Our algorithm outperforms DIPHA, a reference method for the distributed computation of persistence diagrams, with an average speedup of x8 on 512 cores. We show the practical capabilities of our approach by computing the persistence diagram of a public 3D scalar field of 6 billion vertices in 174 seconds on 512 cores. Finally, we provide a usage example of our open-source implementation at https://github.com/eve-le-guillou/DDMS-example.

Problem

• Extend DMS to distributed-memory parallelism for massive datasets
• Develop efficient distributed computations for DMS steps
• Outperform DIPHA in distributed persistence diagram computation

Innovation

• Extends DMS to distributed-memory parallelism
• Introduces self-correcting distributed pairing algorithm
• Uses hybrid MPI+thread approach for scalability