Download or read book Geodesic Convexity in Graphs written by Ignacio M. Pelayo and published by Springer Science & Business Media. This book was released on 2013-09-06 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.
Download or read book Geodesic Convexity in Discrete Spaces written by Azriel Rosenfeld and published by . This book was released on 1994 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A pebbled graph is called '(geodesically) convex' if at least one shortest path between any two unpebbled nodes has no pebbles on any of its nodes. There exist conditions on the node neighborhoods in a pebbled graph that imply convexity; but no such conditions can be necessary for convexity. The convex pebblings can be characterized for various special types of graphs, such as cycles, trees, and cliques. For a graph L whose nodes are the lattice points in the plane under the relation of row or column adjacency, we show that a pebbling of L is convex iff the set of unpebbled nodes is conected and orthoconvex."
Download or read book The Interval Function of a Graph written by H. M. Mulder and published by . This book was released on 1980 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convexity and Graph Theory written by M. Rosenfeld and published by Elsevier. This book was released on 1984-01-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
Download or read book Algorithms and Discrete Applied Mathematics written by Manoj Changat and published by Springer Nature. This book was released on 2020-01-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020, held in Hyderabad, India, in February 2020. The 38 papers presented together with 2 invited talks in this volume were carefully reviewed and selected from 102 submissions. The papers are organized in topical sections on graph algorithms, graph theory, combinatorial optimization, distributed algorithms, combinatorial algorithms, and computational complexity.
Download or read book Strong Doubly Edge Geodetic Problem in Graphs written by D. Antony Xavier and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the computational complexity for strong doubly edge geodetic problem is studied and also some bounds for general graphs are derived.
Download or read book Graph Convexity and Vertex Orderings written by Rachel Jean Selma Anderson and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In discrete mathematics, a convex space is an ordered pair (V,M) where M is a family of subsets of a finite set V , such that: ? ?M, V ?M, and Mis closed under intersection. The elements of M are called convex sets. For a set S ? V , the convex hull of S is the smallest convex set that contains S. A point x of a convex set X is an extreme point of X if X\{x} is also convex. A convex space (V,M) with the property that every convex set is the convex hull of its extreme points is called a convex geometry. A graph G has a P-elimination ordering if an ordering v1, v2, ..., vn of the vertices exists such that vi has property P in the graph induced by vertices vi, vi+1, ..., vn for all i = 1, 2, ...,n. Farber and Jamison [18] showed that for a convex geometry (V,M),X ?M if and only if there is an ordering v1, v2, ..., vk of the points of V ? X such that vi is an extreme point of {vi, vi+1, ..., vk}? X for each i = 1, 2, ...,k. With these concepts in mind, this thesis surveys the literature and summarizes results regarding graph convexities and elimination orderings. These results include classifying graphs for which different types of convexities give convex geometries, and classifying graphs for which different vertex ordering algorithms result in a P-elimination ordering, for P the characteristic property of the extreme points of the convexity. We consider the geodesic, monophonic, m3, 3-Steiner and 3-monophonic convexities, and the vertex ordering algorithms LexBFS, MCS, MEC and MCC. By considering LexDFS, a recently introduced vertex ordering algorithm of Corneil and Krueger [11], we obtain new results: these are characterizations of graphs for which all LexDFS orderings of all induced subgraphs are P-elimination orderings, for every characteristic property P of the extreme vertices for the convexities studied in this thesis.
Download or read book Theory of Convex Structures written by M.L.J. van de Vel and published by Elsevier. This book was released on 1993-08-02 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.
Download or read book Convex Functions and Optimization Methods on Riemannian Manifolds written by C. Udriste and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.
Download or read book Discovery Science written by Poncelet Pascal and published by Springer Nature. This book was released on 2022-11-05 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 25th International Conference on Discovery Science, DS 2022, which took place virtually during October 10-12, 2022. The 27 full papers and 12 short papers presented in this volume were carefully reviewed and selected from 59 submissions.
Download or read book Distance In Graphs written by Fred Buckley and published by Addison Wesley Publishing Company. This book was released on 1990-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Classes written by Andreas Brandstadt and published by SIAM. This book was released on 1999-01-01 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized reference is a definitive encyclopedia for the literature on graph classes. It contains a survey of more than 200 classes of graphs, organized by types of properties used to define and characterize the classes, citing key theorems and literature references for each. The authors state results without proof, providing readers with easy access to far more key theorems than are commonly found in other mathematical texts. Interconnections between graph classes are also provided to make the book useful to a variety of readers.
Download or read book Machine Learning and Knowledge Discovery in Databases written by Massih-Reza Amini and published by Springer Nature. This book was released on 2023-03-16 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The multi-volume set LNAI 13713 until 13718 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2022, which took place in Grenoble, France, in September 2022. The 236 full papers presented in these proceedings were carefully reviewed and selected from a total of 1060 submissions. In addition, the proceedings include 17 Demo Track contributions. The volumes are organized in topical sections as follows: Part I: Clustering and dimensionality reduction; anomaly detection; interpretability and explainability; ranking and recommender systems; transfer and multitask learning; Part II: Networks and graphs; knowledge graphs; social network analysis; graph neural networks; natural language processing and text mining; conversational systems; Part III: Deep learning; robust and adversarial machine learning; generative models; computer vision; meta-learning, neural architecture search; Part IV: Reinforcement learning; multi-agent reinforcement learning; bandits and online learning; active and semi-supervised learning; private and federated learning; Part V: Supervised learning; probabilistic inference; optimal transport; optimization; quantum, hardware; sustainability; Part VI: Time series; financial machine learning; applications; applications: transportation; demo track.
Download or read book Algorithms for Convex Optimization written by Nisheeth K. Vishnoi and published by Cambridge University Press. This book was released on 2021-10-07 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Download or read book Topics in Combinatorics and Graph Theory written by Rainer Bodendiek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory is a part of discrete mathematics characterized by the fact of an extremely rapid development during the last 10 years. The number of graph theoretical paper as well as the number of graph theorists increase very strongly. The main purpose of this book is to show the reader the variety of graph theoretical methods and the relation to combinatorics and to give him a survey on a lot of new results, special methods, and interesting informations. This book, which grew out of contributions given by about 130 authors in honour to the 70th birthday of Gerhard Ringel, one of the pioneers in graph theory, is meant to serve as a source of open problems, reference and guide to the extensive literature and as stimulant to further research on graph theory and combinatorics.
Download or read book Combinatorial Algorithms written by Sun-Yuan Hsieh and published by Springer Nature. This book was released on 2023-06-02 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 34th International Workshop on Combinatorial Algorithms, IWOCA 2023, held in Tainan, Taiwan, during June 7–10, 2023. The 33 full papers included in this book were carefully reviewed and selected from 86 submissions. They were organized in topical sections as follows: algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theory and temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic and randomized algorithms; and streaming algorithms.
