09061 Abstracts Collection -- Combinatorial Scientific Computing

From 01.02.2009 to 06.02.2009, the Dagstuhl Seminar 09061 ``Combinatorial Scientific Computing \u27\u27 was held in Schloss Dagstuhl -- Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

New Graph Algorithms via Polyhedral Techniques

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. Somewhat surprisingly, similar polyhedral techniques can be harnessed in the two seemingly disparate settings. In the first part of the thesis we address a benchmark problem in combinatorial optimization: the asymmetric traveling salesman problem (ATSP). It consists in finding the shortest tour that visits all vertices of a given directed graph with weights on edges. Due to its NP-hardness, the theoretical study of algorithms for ATSP has focused on approximation algorithms: ones that are provably both efficient and give solutions competitive with the optimum. Specifically, a rho-approximation algorithm for ATSP is one that runs in polynomial time and always outputs a tour that is at most rho times longer than the shortest tour. Finding such an approximation algorithm with rho bounded (i.e., a constant factor) had been a long-standing open problem. In this thesis, we give such an algorithm. Our approximation guarantee is analyzed with respect to the standard linear programming relaxation, and thus our result also confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics due to Svensson. In particular, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. This reduction takes advantage of a laminar family of vertex sets that arises from the linear programming relaxation. In the second part of the thesis we address the perfect matching problem. The first polynomial-time algorithm for it, given by Edmonds in 1965, is historically associated with the introduction of the class P and our notion that ``polynomial-time'' means ``efficient''. That algorithm is sequential and deterministic. We have also known since the 1980s that the matching problem has efficient parallel algorithms if the use of randomness is allowed. Formally, it is in the class RNC, i.e., it has randomized algorithms that use polynomially many processors and run in polylogarithmic time. However, we do not know if randomness is necessary - that is, whether the matching problem is in the class NC. In this thesis we show that the matching problem is in quasi-NC. That is, we give a deterministic parallel algorithm that runs in O(log^3 n) time on n^{O(log^2 n)} processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani to obtain an RNC algorithm. Our proof extends the framework of Fenner, Gurjar and Thierauf, who proved the analogous result in the special case of bipartite graphs. Compared to that setting, several new ingredients are needed due to the significantly more complex structure of perfect matchings in general graphs. In particular, our proof heavily relies on the laminar structure of the faces of the perfect matching polytope

Vermeidung von Repräsentationsheterogenitäten in realweltlichen Wissensgraphen

Knowledge graphs are repositories providing factual knowledge about entities. They are a great source of knowledge to support modern AI applications for Web search, question answering, digital assistants, and online shopping. The advantages of machine learning techniques and the Web's growth have led to colossal knowledge graphs with billions of facts about hundreds of millions of entities collected from a large variety of sources. While integrating independent knowledge sources promises rich information, it inherently leads to heterogeneities in representation due to a large variety of different conceptualizations. Thus, real-world knowledge graphs are threatened in their overall utility. Due to their sheer size, they are hardly manually curatable anymore. Automatic and semi-automatic methods are needed to cope with these vast knowledge repositories. We first address the general topic of representation heterogeneity by surveying the problem throughout various data-intensive fields: databases, ontologies, and knowledge graphs. Different techniques for automatically resolving heterogeneity issues are presented and discussed, while several open problems are identified. Next, we focus on entity heterogeneity. We show that automatic matching techniques may run into quality problems when working in a multi-knowledge graph scenario due to incorrect transitive identity links. We present four techniques that can be used to improve the quality of arbitrary entity matching tools significantly. Concerning relation heterogeneity, we show that synonymous relations in knowledge graphs pose several difficulties in querying. Therefore, we resolve these heterogeneities with knowledge graph embeddings and by Horn rule mining. All methods detect synonymous relations in knowledge graphs with high quality. Furthermore, we present a novel technique for avoiding heterogeneity issues at query time using implicit knowledge storage. We show that large neural language models are a valuable source of knowledge that is queried similarly to knowledge graphs already solving several heterogeneity issues internally.Wissensgraphen sind eine wichtige Datenquelle von Entitätswissen. Sie unterstützen viele moderne KI-Anwendungen. Dazu gehören unter anderem Websuche, die automatische Beantwortung von Fragen, digitale Assistenten und Online-Shopping. Neue Errungenschaften im maschinellen Lernen und das außerordentliche Wachstum des Internets haben zu riesigen Wissensgraphen geführt. Diese umfassen häufig Milliarden von Fakten über Hunderte von Millionen von Entitäten; häufig aus vielen verschiedenen Quellen. Während die Integration unabhängiger Wissensquellen zu einer großen Informationsvielfalt führen kann, führt sie inhärent zu Heterogenitäten in der Wissensrepräsentation. Diese Heterogenität in den Daten gefährdet den praktischen Nutzen der Wissensgraphen. Durch ihre Größe lassen sich die Wissensgraphen allerdings nicht mehr manuell bereinigen. Dafür werden heutzutage häufig automatische und halbautomatische Methoden benötigt. In dieser Arbeit befassen wir uns mit dem Thema Repräsentationsheterogenität. Wir klassifizieren Heterogenität entlang verschiedener Dimensionen und erläutern Heterogenitätsprobleme in Datenbanken, Ontologien und Wissensgraphen. Weiterhin geben wir einen knappen Überblick über verschiedene Techniken zur automatischen Lösung von Heterogenitätsproblemen. Im nächsten Kapitel beschäftigen wir uns mit Entitätsheterogenität. Wir zeigen Probleme auf, die in einem Multi-Wissensgraphen-Szenario aufgrund von fehlerhaften transitiven Links entstehen. Um diese Probleme zu lösen stellen wir vier Techniken vor, mit denen sich die Qualität beliebiger Entity-Alignment-Tools deutlich verbessern lässt. Wir zeigen, dass Relationsheterogenität in Wissensgraphen zu Problemen bei der Anfragenbeantwortung führen kann. Daher entwickeln wir verschiedene Methoden um synonyme Relationen zu finden. Eine der Methoden arbeitet mit hochdimensionalen Wissensgrapheinbettungen, die andere mit einem Rule Mining Ansatz. Beide Methoden können synonyme Relationen in Wissensgraphen mit hoher Qualität erkennen. Darüber hinaus stellen wir eine neuartige Technik zur Vermeidung von Heterogenitätsproblemen vor, bei der wir eine implizite Wissensrepräsentation verwenden. Wir zeigen, dass große neuronale Sprachmodelle eine wertvolle Wissensquelle sind, die ähnlich wie Wissensgraphen angefragt werden können. Im Sprachmodell selbst werden bereits viele der Heterogenitätsprobleme aufgelöst, so dass eine Anfrage heterogener Wissensgraphen möglich wird

Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing

Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM