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

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 sing...

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Veröffentlicht in:	IEEE transactions on parallel and distributed systems Jg. 37; H. 1; S. 137 - 154
Hauptverfasser:	Le Guillou, Eve, Fortin, Pierre, Tierny, Julien
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	IEEE 01.01.2026 Institute of Electrical and Electronics Engineers
Schlagworte:	Computational efficiency Computer Science Data structures Distributed algorithms Distributed databases distributed-memory algorithms Faces Filtration Hands high-performance computing Parallel processing persistent homology Three-dimensional displays Topological data analysis Topology distributed-memory algorithms Topological data analysis high-performance computing persistent homology
ISSN:	1045-9219, 1558-2183
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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 <inline-formula><tex-math notation="LaTeX">\times 8</tex-math> <mml:math><mml:mrow><mml:mo>×</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="leguillou-ieq1-3626047.gif"/> </inline-formula> 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 .
AbstractList	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 <inline-formula><tex-math notation="LaTeX">\times 8</tex-math> <mml:math><mml:mrow><mml:mo>×</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="leguillou-ieq1-3626047.gif"/> </inline-formula> 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 . 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 ×8 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.
Author	Le Guillou, Eve Fortin, Pierre Tierny, Julien
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Keywords	distributed-memory algorithms Topological data analysis high-performance computing persistent homology
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Snippet	The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich"... The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The “Discrete Morse Sandwich”...
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SubjectTerms	Computational efficiency Computer Science Data structures Distributed algorithms Distributed databases distributed-memory algorithms Faces Filtration Hands high-performance computing Parallel processing persistent homology Three-dimensional displays Topological data analysis Topology
Title	Distributed Discrete Morse Sandwich: Efficient Computation of Persistence Diagrams for Massive Scalar Data
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