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

TL;DR

This paper extends the Discrete Morse Sandwich method to distributed-memory systems, enabling scalable and efficient computation of persistence diagrams for massive 3D scalar datasets across multiple compute nodes.

Contribution

We developed a distributed-memory parallel version of DMS with new algorithms and data structures, significantly improving scalability and performance for large datasets.

Findings

Achieved up to 8x speedup over DIPHA on 512 cores

Successfully computed a 6-billion-vertex dataset in 174 seconds

Demonstrated scalability up to 16 nodes with 512 cores

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.