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Hypergraph Theory

Hypergraph Theory PDF Author: Alain Bretto
Publisher: Springer Science & Business Media
ISBN: 3319000802
Category : Mathematics
Languages : en
Pages : 119

Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.

Hypergraph Theory

Hypergraph Theory PDF Author: Alain Bretto
Publisher: Springer Science & Business Media
ISBN: 3319000802
Category : Mathematics
Languages : en
Pages : 119

Book Description
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.

Introduction to Graph and Hypergraph Theory

Introduction to Graph and Hypergraph Theory PDF Author: Vitaly Ivanovich Voloshin
Publisher:
ISBN: 9781606923726
Category : Graph theory
Languages : en
Pages : 287

Book Description
This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalisation of Part I. The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring. The second part considers generalisations of Part I and discusses hypertrees, bipartite hypergraphs, hypercycles, chordal hypergraphs, planar hypergraphs and hypergraph colouring. There is an interaction between the parts and within the parts to show how ideas of generalisations work. The main point is to exhibit the ways of generalisations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hypergraphs. This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hypergraphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view.

Advances in Imaging and Electron Physics

Advances in Imaging and Electron Physics PDF Author: Peter W. Hawkes
Publisher: Elsevier
ISBN: 9780080490090
Category : Technology & Engineering
Languages : en
Pages : 247

Book Description
The subjects reviewed in the Advances in Imaging and Electron Physics series cover a broad range of themes including microscopy, electromagnetic fields and image coding. This book is essential reading for electrical engineers, applied mathematicians and robotics experts. Emphasizes broad and in depth article collaborations between world-renowned scientists in the field of image and electron physics Presents theory and it's application in a practical sense, providing long awaited solutions and new findings Bridges the gap between academic researchers and R&D designers by addressing and solving daily issues

Graphs and Combinatorial Optimization: from Theory to Applications

Graphs and Combinatorial Optimization: from Theory to Applications PDF Author: Claudio Gentile
Publisher: Springer Nature
ISBN: 3030630722
Category : Mathematics
Languages : en
Pages : 408

Book Description
This book highlights new and original contributions on Graph Theory and Combinatorial Optimization both from the theoretical point of view and from applications in all fields. The book chapters describe models and methods based on graphs, structural properties, discrete optimization, network optimization, mixed-integer programming, heuristics, meta-heuristics, math-heuristics, and exact methods as well as applications. The book collects selected contributions from the CTW2020 international conference (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization), held online on September 14-16, 2020. The conference was organized by IASI-CNR with the contribution of University of Roma Tre, University Roma Tor Vergata, and CNRS-LIX and with the support of AIRO. It is addressed to researchers, PhD students, and practitioners in the fields of Graph Theory, Discrete Mathematics, Combinatorial Optimization, and Operations Research.

Tensor Analysis

Tensor Analysis PDF Author: Liqun Qi
Publisher: SIAM
ISBN: 1611974747
Category : Mathematics
Languages : en
Pages : 313

Book Description
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. ?

Bio-Inspired Computing: Theories and Applications

Bio-Inspired Computing: Theories and Applications PDF Author: Linqiang Pan
Publisher: Springer Nature
ISBN: 9811613540
Category : Computers
Languages : en
Pages : 653

Book Description
This volume constitutes the revised selected papers of the 15th International Conference on Bio-inspired Computing: Theories and Applications, BIC-TA 2020, held in Qingdao, China, in October 2020. The 43 full papers presented in both volumes were selected from 109 submissions. The papers are organized according to the topical headings: evolutionary computation and swarm intelligence; neural networks and machine learning; DNA computing and membrane computing.

Decision Making Based on Valued Fuzzy Superhypergraphs

Decision Making Based on Valued Fuzzy Superhypergraphs PDF Author: Mohammad Hamidi
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 17

Book Description
This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy (hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphs as complex superhypernetworks in order to make a relation between labeled objects in the form of details and generalities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzes them in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole to the whole group of objects at the same time. We have investigated the properties of fuzzy (quasi) superhypergraphs based on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valued fuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based on the permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi) superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introduced in this study and it is applied in designing the real problem in the real world. Finally, the problem of business superhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.

Graph-Theoretic Problems and Their New Applications

Graph-Theoretic Problems and Their New Applications PDF Author: Frank Werner
Publisher: MDPI
ISBN: 3039287982
Category : Technology & Engineering
Languages : en
Pages : 294

Book Description
Graph theory is an important area of applied mathematics with a broad spectrum of applications in many fields. This book results from aSpecialIssue in the journal Mathematics entitled “Graph-Theoretic Problems and Their New Applications”. It contains 20 articles covering a broad spectrum of graph-theoretic works that were selected from 151 submitted papers after a thorough refereeing process. Among others, it includes a deep survey on mixed graphs and their use for solutions ti scheduling problems. Other subjects include topological indices, domination numbers of graphs, domination games, contraction mappings, and neutrosophic graphs. Several applications of graph theory are discussed, e.g., the use of graph theory in the context of molecular processes.

Learning and Intelligent Optimization: Designing, Implementing and Analyzing Effective Heuristics

Learning and Intelligent Optimization: Designing, Implementing and Analyzing Effective Heuristics PDF Author: Thomas Stützle
Publisher: Springer Science & Business Media
ISBN: 3642111688
Category : Computers
Languages : en
Pages : 284

Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on Learning and Intelligent Optimization, LION 2009 III, held in Trento, Italy, in January 2009. The 15 revised full papers, one extended abstract and two poster sessions were carefully reviewed and selected from 86 submissions for inclusion in the book. The papers cover current issues of stochastic local search methods and meta-heuristics, hybridizations of constraint and mathematical programming with meta-heuristics, supervised, unsupervised and reinforcement learning applied to heuristic search, reactive search (online self-tuning methods), algorithm portfolios and off-line tuning methods, algorithms for dynamic, stochastic and multi-objective problems, interface(s) between discrete and continuous optimization, experimental analysis and modeling of algorithms, theoretical foundations, parallelization of optimization algorithms, memory-based optimization, prohibition-based methods (tabu search), memetic algorithms, evolutionary algorithms, dynamic local search, iterated local search, variable neighborhood search and swarm intelligence methods (ant colony optimization, particle swarm optimization etc.).

Handbook of Combinatorics

Handbook of Combinatorics PDF Author: R.L. Graham
Publisher: Elsevier
ISBN: 008093384X
Category : Mathematics
Languages : en
Pages : 1018

Book Description
Handbook of Combinatorics