Topology Discovery of Sparse Random Graphs With Few Participants

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is scheduled to appear in J. on Random Structures and Algorithm

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

An analytical comparison of coalescent-based multilocus methods: The three-taxon case

Incomplete lineage sorting (ILS) is a common source of gene tree incongruence in multilocus analyses. A large number of methods have been developed to infer species trees in the presence of ILS. Here we provide a mathematical analysis of several coalescent-based methods. Our analysis is performed on a three-taxon species tree and assumes that the gene trees are correctly reconstructed along with their branch lengths

Efficient seeding techniques for protein similarity search

We apply the concept of subset seeds proposed in [1] to similarity search in protein sequences. The main question studied is the design of efficient seed alphabets to construct seeds with optimal sensitivity/selectivity trade-offs. We propose several different design methods and use them to construct several alphabets.We then perform an analysis of seeds built over those alphabet and compare them with the standard Blastp seeding method [2,3], as well as with the family of vector seeds proposed in [4]. While the formalism of subset seed is less expressive (but less costly to implement) than the accumulative principle used in Blastp and vector seeds, our seeds show a similar or even better performance than Blastp on Bernoulli models of proteins compatible with the common BLOSUM62 matrix