Task-based Augmented Contour Trees with Fibonacci Heaps

This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of contour tree based applications including data segmentation. Our approach completely revisits the traditional, sequential contour tree algorithm to re-formulate all the steps of the computation as a set of independent local tasks. This includes a new computation procedure based on Fibonacci heaps for the join and split trees, two intermediate data structures used to compute the contour tree, whose constructions are efficiently carried out concurrently thanks to the dynamic scheduling of task parallelism. We also introduce a new parallel algorithm for the combination of these two trees into the output global contour tree. Overall, this results in superior time performance in practice, both in sequential and in parallel thanks to the OpenMP task runtime. We report performance numbers that compare our approach to reference sequential and multi-threaded implementations for the computation of augmented merge and contour trees. These experiments demonstrate the run-time efficiency of our approach and its scalability on common workstations. We demonstrate the utility of our approach in data segmentation applications

Task-based Augmented Reeb Graphs with Dynamic ST-Trees

International audienceThis paper presents, to the best of our knowledge, the first parallel algorithm for the computation of the augmented Reeb graph of piecewise linear scalar data. Such augmented Reeb graphs have a wide range of applications , including contour seeding and feature based segmentation. Our approach targets shared-memory multi-core workstations. For this, it completely revisits the optimal, but sequential, Reeb graph algorithm, which is capable of handing data in arbitrary dimension and with optimal time complexity. We take advantage of Fibonacci heaps to exploit the ST-Tree data structure through independent local propagations, while maintaining the optimal, linearithmic time complexity of the sequential reference algorithm. These independent propagations can be expressed using OpenMP tasks, hence benefiting in parallel from the dynamic load balancing of the task runtime while enabling us to increase the parallelism degree thanks to a dual sweep. We present performance results on triangulated surfaces and tetrahedral meshes. We provide comparisons to related work and show that our new algorithm results in superior time performance in practice, both in sequential and in parallel. An open-source C++ implementation is provided for reproducibility

Towards Distributed Task-based Visualization and Data Analysis

To support scientific work with large and complex data the field of scientific visualization emerged in computer science and produces images through computational analysis of the data. Frameworks for combination of different analysis and visualization modules allow the user to create flexible pipelines for this purpose and set the standard for interactive scientific visualization used by domain scientists. Existing frameworks employ a thread-parallel message-passing approach to parallel and distributed scalability, leaving the field of scientific visualization in high performance computing to specialized ad-hoc implementations. The task-parallel programming paradigm proves promising to improve scalability and portability in high performance computing implementations and thus, this thesis aims towards the creation of a framework for distributed, task-based visualization modules and pipelines. The major contribution of the thesis is the establishment of modules for Merge Tree construction and (based on the former) topological simplification. Such modules already form a necessary first step for most visualization pipelines and can be expected to increase in importance for larger and more complex data produced and/or analysed by high performance computing. To create a task-parallel, distributed Merge Tree construction module the construction process has to be completely revised. We derive a novel property of Merge Tree saddles and introduce a novel task-parallel, distributed Merge Tree construction method that has both good performance and scalability. This forms the basis for a module for topological simplification which we extend by introducing novel alternative simplification parameters that aim to reduce the importance of prior domain knowledge to increase flexibility in typical high performance computing scenarios. Both modules lay the groundwork for continuative analysis and visualization steps and form a fundamental step towards an extensive task-parallel visualization pipeline framework for high performance computing.Wissenschaftliche Visualisierung ist eine Disziplin der Informatik, die durch computergestützte Analyse Bilder aus Datensätzen erzeugt, um das wissenschaftliche Arbeiten mit großen und komplexen Daten zu unterstützen. Softwaresysteme, die dem Anwender die Kombination verschiedener Analyse- und Visualisierungsmodule zu einer flexiblen Pipeline erlauben, stellen den Standard für interaktive wissenschaftliche Visualisierung. Die hierfür bereits existierenden Systeme setzen auf Thread-Parallelisierung mit expliziter Kommunikation, sodass das Feld der wissenschaftlichen Visualisierung auf Hochleistungsrechnern meist spezialisierten Direktlösungen überlassen wird. An dieser Stelle scheint Task-Parallelisierung vielversprechend, um Skalierbarkeit und Übertragbarkeit von Lösungen für Hochleistungsrechner zu verbessern. Daher zielt die vorliegende Arbeit auf die Umsetzung eines Softwaresystems für verteilte und task-parallele Visualisierungsmodule und -pipelines ab. Der zentrale Beitrag den die vorliegende Arbeit leistet ist die Einführung zweier Module für Merge Tree Konstruktion und topologische Datenbereinigung. Solche Module stellen bereits einen notwendigen ersten Schritt für die meisten Visualisierungspipelines dar und werden für größere und komplexere Datensätze, die im Hochleistungsrechnen erzeugt beziehungsweise analysiert werden, erwartungsgemäß noch wichtiger. Um eine Task-parallele, verteilbare Konstruktionsmethode für Merge Trees zu entwickeln musste der etablierte Algorithmus grundlegend überarbeitet werden. In dieser Arbeit leiten wir eine neue Eigenschaft für Merge Tree Knoten her und entwickeln einen neuartigen Konstruktionsalgorithmus, der gute Performance und Skalierbarkeit aufweist. Darauf aufbauend entwickeln wir ein Modul für topologische Datenbereinigung, welche wir durch neue, alternative Bereinigungsparameter erweitern, um die Flexibilität im Einstaz auf Hochleistungsrechnern zu erhöhen. Beide Module ermöglichen weiterführende Analyse und Visualisierung und setzen einen Grundstein für die Entwicklung eines umfassenden Task-parallelen Softwaresystems für Visualisierungspipelines auf Hochleistungsrechnern

Parallel Mapper

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method

Statistical Parameter Selection for Clustering Persistence Diagrams

International audienceIn urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering so-called persistence diagrams, which are reduced representations of the original data, motivated by the extraction of topological features. Based on a recently published progressive algorithm for the clustering of persistence diagrams, we determine the optimal number of clusters, and therefore the number of significantly different outcome scenarios, by the minimization of established statistical score functions. Furthermore, we present a proof-of-concept prototype implementation of the statistical selection of the number of clusters and provide the results of an experimental study, where this implementation has been applied to real-world ensemble data sets