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Author : Pierre Kelsen
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (31 download)
Download or read book Efficient Computation of Extremal Structures in Graphs and Hypergraphs written by Pierre Kelsen and published by . This book was released on 1993 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xu Liu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.4/5 (64 download)
Download or read book Structure Detection in Graphs and Hypergraphs written by Xu Liu and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding relationships among entities in large-scale systems is a fundamental operation in data science. Such systems can be modeled as graphs if the relationships are pairwise or as hypergraphs if the relationships are multi-way. Structures in graphs and hypergraphs such as communities or connected components and metrics such as centrality indices encapsulate relationships among entities. For community detection and connected components decomposition, in graphs and hypergraphs, as the sizes of the systems continue to increase, we generally need fast algorithms to enable large-scale real-time processing. The first goal of this thesis is to develop linear-time algorithms that can be used to detect communities and connected components in graphs. We achieve this by developing a new framework based on Direction-optimizing Label Propagation Algorithm (DOLPA). We parallelize DOLPA in both shared-memory and distributed-memory. Since community detection is NP-hard, it is difficult for community detection algorithms to achieve both high quality of solution and fast convergence at the same time. As the second goal of this thesis, DOLPA provides a trade-off to accommodate different community detection scenarios: accurate detection versus fast detection.The other two goals of the thesis target hypergraphs. Hypergraphs are increasingly becoming important in data science applications due to their capability for robust data representation. However, their computational complexity can be high. To reduce this complexity, lower-dimensional approximations of hypergraphs to compute relevant structures are needed. Line graphs, in particular, high order s-line graphs for s > 1 of hypergraphs are a critical tool for this purpose, since they capture important hypergraph properties. Obtaining high order s-line graphs is highly compute-intensive and irregular. Until recently, no efficient algorithm has been proposed to compute s-line graphs for s 9́Æ 2. The third goal of this thesis is to develop a scalable framework for s-line graph computation and s-metrics computation for arbitrary s values. The framework is applied for hypergraph structure detection in real-world systems. The last goal of the thesis is to design algorithms to speedup s-line graph computation. The new algorithms are orders of magnitude faster than a naive algorithm and the SpGEMM algorithm with filtration.
Author : Qionghai Dai
Publisher : Springer Nature
ISBN 13 : 9819901855
Total Pages : 251 pages
Book Rating : 4.8/5 (199 download)
Download or read book Hypergraph Computation written by Qionghai Dai and published by Springer Nature. This book was released on 2023-06-16 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book discusses the theory and methods of hypergraph computation. Many underlying relationships among data can be represented using graphs, for example in the areas including computer vision, molecular chemistry, molecular biology, etc. In the last decade, methods like graph-based learning and neural network methods have been developed to process such data, they are particularly suitable for handling relational learning tasks. In many real-world problems, however, relationships among the objects of our interest are more complex than pair-wise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for learning tasks. Hypergraph, as a generation of graph, has shown superior performance on modelling complex correlations compared with graph. Recent years have witnessed a great popularity of researches on hypergraph-related AI methods, which have been used in computer vision, social media analysis, etc. We summarize these attempts as a new computing paradigm, called hypergraph computation, which is to formulate the high-order correlations underneath the data using hypergraph, and then conduct semantic computing on the hypergraph for different applications. The content of this book consists of hypergraph computation paradigms, hypergraph modelling, hypergraph structure evolution, hypergraph neural networks, and applications of hypergraph computation in different fields. We further summarize recent achievements and future directions on hypergraph computation in this book.
Author : Liqun Qi
Publisher : SIAM
ISBN 13 : 1611974755
Total Pages : 313 pages
Book Rating : 4.6/5 (119 download)
Download or read book Tensor Analysis written by Liqun Qi and published by SIAM. This book was released on 2017-04-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.
Author : Amites Sarkar
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (894 download)
Download or read book Extremal Problems for Graphs and Hypergraphs written by Amites Sarkar and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (4 download)
Download or read book Publications of the State of Illinois written by and published by . This book was released on 1993 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tibor Szabó
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (355 download)
Download or read book Extremal Problems for Graphs and Hypergraphs written by Tibor Szabó and published by . This book was released on 1996 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ronald Peikert
Publisher : Springer Science & Business Media
ISBN 13 : 3642231756
Total Pages : 299 pages
Book Rating : 4.6/5 (422 download)
Download or read book Topological Methods in Data Analysis and Visualization II written by Ronald Peikert and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.
Author : Library of Congress. Exchange and Gift Division
Publisher :
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4.3/5 ( download)
Download or read book Monthly Checklist of State Publications written by Library of Congress. Exchange and Gift Division and published by . This book was released on 1993 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual index to the monographs appears early in the following year.
Author : נוגה אלון
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (498 download)
Download or read book Extremal problems in graphs and hypergraphs written by נוגה אלון and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Timothy Duncan Townsend
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Extremal Problems on Graphs, Directed Graphs and Hypergraphs written by Timothy Duncan Townsend and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 294 pages
Book Rating : 4.3/5 (243 download)
Download or read book Illinois Documents List written by and published by . This book was released on 1993 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Takeshi Tokuyama
Publisher : Springer
ISBN 13 : 3540771204
Total Pages : 945 pages
Book Rating : 4.5/5 (47 download)
Download or read book Algorithms and Computation written by Takeshi Tokuyama and published by Springer. This book was released on 2007-12-06 with total page 945 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Symposium on Algorithms and Computation, ISAAC 2007, held in Sendai, Japan, in December 2007. The 77 revised full papers presented together with two invited talks were carefully reviewed and selected from 220 submissions. The papers included topical sections on graph algorithms, computational geometry, complexity, graph drawing, distributed algorithms, optimization, data structure, and game theory.
Author : Komei Fukuda
Publisher : Springer
ISBN 13 : 3642155820
Total Pages : 382 pages
Book Rating : 4.6/5 (421 download)
Download or read book Mathematical Software - ICMS 2010 written by Komei Fukuda and published by Springer. This book was released on 2010-09-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Congress on Mathematical Software, ICMS 2010, held in Kobe, Japan in September 2010. The 49 revised full papers presented were carefully reviewed and selected for presentation. The papers are organized in topical sections on computational group theory, computation of special functions, computer algebra and reliable computing, computer tools for mathematical editing and scientific visualization, exact numeric computation for algebraic and geometric computation, formal proof, geometry and visualization, Groebner bases and applications, number theoretical software as well as software for optimization and polyhedral computation.
Author : University of Illinois at Urbana-Champaign. Engineering Documents Center
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.U/5 (183 download)
Download or read book Engineering Documents Center Index written by University of Illinois at Urbana-Champaign. Engineering Documents Center and published by . This book was released on 1993 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tetsuo Asano
Publisher : Springer Science & Business Media
ISBN 13 : 9783540620488
Total Pages : 470 pages
Book Rating : 4.6/5 (24 download)
Download or read book Algorithms and Computation written by Tetsuo Asano and published by Springer Science & Business Media. This book was released on 1996-11-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today the cemented joint prosthesis operation is one of the most frequent procedures in orthopaedic surgery. During the past 30 years the individual steps of such an operation have been carefully validated and thus allow for a reproducible and standardized operation, including a reliable prognosis for the maintenance of the joint. This manual is a practical guide to a complication preventing cementing technique, cement fixation, maintenance of the bone and diamond technique. Clear drawings and diagrams guide the reader through the pre-operative, peri-operative and post-operative steps. The manual covers all possible complications and gives clear instructions, so as to prevent complications but also to cope with them if they occur. Finally, it covers all forensic criteria to be considered.
Author : C. Berge
Publisher : Elsevier
ISBN 13 : 0080880231
Total Pages : 267 pages
Book Rating : 4.0/5 (88 download)
Download or read book Hypergraphs written by C. Berge and published by Elsevier. This book was released on 1984-05-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.
