arXiv subjects

Pierre Guillou

Publications and source records attributed to Pierre Guillou.

3 recordsLinked to original sources

arXiv2023

TTK is Getting MPI-Ready

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.

cs.DC↗

arXiv2022

Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark

This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field $f$ defined on a $d$-dimensional simplicial complex $K$, with $d \leq 3$. Our work revisits the seminal algorithm "PairSimplices" [31], [103] with discrete Morse theory (DMT) [34], [80], which greatly reduces the number of input simplices to consider. Further, we also extend to DMT and accelerate the stratification strategy described in "PairSimplices" for the fast computation of the $0^{th}$ and $(d - 1)^{th}$ diagrams, noted $D_0(f)$ and $D_{d-1}(f)$. Minima-saddle persistence pairs ($D_0(f)$) and saddle-maximum persistence pairs ($D_{d-1}(f)$) are efficiently computed by processing, with a Union-Find, the unstable sets of $1$-saddles and the stable sets of $(d - 1)$-saddles. This fast pre-computation for the dimensions $0$ and $(d - 1)$ enables an aggressive specialization of [4] to the 3D case, which results in a drastic reduction of the number of input simplices for the computation of $D_1(f)$, the intermediate layer of the sandwich. Finally, we document several performance improvements via shared-memory parallelism. We provide an open-source implementation of our algorithm for reproducibility purposes. We also contribute a reproducible benchmark package, which exploits three-dimensional data from a public repository and compares our algorithm to a variety of publicly available implementations. Extensive experiments indicate that our algorithm improves by two orders of magnitude the time performance of the seminal "PairSimplices" algorithm it extends. Moreover, it also improves memory footprint and time performance over a selection of 14 competing approaches, with a substantial gain over the fastest available approaches, while producing a strictly identical output.

cs.LG↗

arXiv2021

A Progressive Approach to Scalar Field Topology

This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are vertices that have no impact on the topological description of the data and for which we show that no computation is required as they are introduced in the hierarchy. This enables the definition of efficient coarse-to-fine topological algorithms, which leverage fast update mechanisms for ordinary vertices and avoid computation for the topologically invariant ones. We demonstrate our approach with two examples of topological algorithms (critical point extraction and persistence diagram computation), which generate interpretable outputs upon interruption requests and which progressively refine them otherwise. Experiments on real-life datasets illustrate that our progressive strategy, in addition to the continuous visual feedback it provides, even improves run time performance with regard to non-progressive algorithms and we describe further accelerations with shared-memory parallelism. We illustrate the utility of our approach in batch-mode and interactive setups, where it respectively enables the control of the execution time of complete topological pipelines as well as previews of the topological features found in a dataset, with progressive updates delivered within interactive times.

cs.GR↗