# TTK is Getting MPI-Ready

arXiv: https://arxiv.org/abs/2310.08339 · HTML: https://mlsanity.com/paper/2310.08339/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 78 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Wasserstein Distances, Geodesics and Barycenters of Merge Trees](https://mlsanity.com/paper/2107.07789/) (2021)
- [Task-based Augmented Contour Trees with Fibonacci Heaps](https://mlsanity.com/paper/1902.04805/) (2019)
- [Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings](https://mlsanity.com/paper/1908.07841/) (2019)
- [TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data](https://mlsanity.com/paper/2009.01512/) (2020)
- [Distributed computation of persistent homology](https://mlsanity.com/paper/1310.0710/) (2013)
- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study](https://mlsanity.com/paper/2207.14080/) (2022)
- [Localized Topological Simplification of Scalar Data](https://mlsanity.com/paper/2009.00083/) (2020)
- [Topological data analysis of vortices in the magnetically-induced current density in LiH molecule](https://mlsanity.com/paper/2212.08690/) (2022)
- [Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)](https://mlsanity.com/paper/2207.10960/) (2022)
- [Topologically Controlled Lossy Compression](https://mlsanity.com/paper/1802.02731/) (2018)
- [Wasserstein Dictionaries of Persistence Diagrams](https://mlsanity.com/paper/2304.14852/) (2023)
- [Parallel Computation of Piecewise Linear Morse-Smale Segmentations](https://mlsanity.com/paper/2303.15491/) (2023)
- [Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)](https://mlsanity.com/paper/2307.02509/) (2023)
- [Merge Tree Geodesics and Barycenters with Path Mappings](https://mlsanity.com/paper/2308.03672/) (2023)
- [A Task-Parallel Approach for Localized Topological Data Structures](https://mlsanity.com/paper/2308.15638/) (2023)

## Built on by (most cited first, 3 of 3)

- [Identifying Locally Turbulent Vortices within Instabilities](https://mlsanity.com/paper/2408.12662/) (2024)
- [Continuous Edit Distance, Geodesics and Barycenters of Time-varying Persistence Diagrams](https://mlsanity.com/paper/2512.12939/) (2025)
- [Sierpi'nski--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation](https://mlsanity.com/paper/2609.01528/) (2026)

## Abstract (arXiv)

This system paper documents the technical foundations for the extension of the Topology ToolKit (TTK) to distributed-memory parallelism with the Message Passing Interface (MPI). While several recent papers introduced topology-based approaches for distributed-memory environments, these were reporting experiments obtained with tailored, mono-algorithm implementations. In contrast, we describe in this paper a versatile approach (supporting both triangulated domains and regular grids) for the support of topological analysis pipelines, i.e. a sequence of topological algorithms interacting together. While developing this extension, we faced several algorithmic and software engineering challenges, which we document in this paper. We describe an MPI extension of TTK's data structure for triangulation representation and traversal, a central component to the global performance and generality of TTK's topological implementations. We also introduce an intermediate interface between TTK and MPI, both at the global pipeline level, and at the fine-grain algorithmic level. We provide a taxonomy for the distributed-memory topological algorithms supported by TTK, depending on their communication needs and provide examples of hybrid MPI+thread parallelizations. Performance analyses show that parallel efficiencies range from 20% to 80% (depending on the algorithms), and that the MPI-specific preconditioning introduced by our framework induces a negligible computation time overhead. We illustrate the new distributed-memory capabilities of TTK with an example of advanced analysis pipeline, combining multiple algorithms, run on the largest publicly available dataset we have found (120 billion vertices) on a cluster with 64 nodes (for a total of 1536 cores). Finally, we provide a roadmap for the completion of TTK's MPI extension, along with generic recommendations for each algorithm communication category.