Path Problems In Networks
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| Author | : John S. Baras |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 78 |
| Release | : 2009-10-15 |
| Genre | : Computers |
| ISBN | : 1598299239 |
The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path problem, and an exposition of a broad range of applications. First of all, the shortest path problem is presented so as to fix terminology and concepts: existence and uniqueness of solutions, robustness to parameter changes, and centralized and distributed computation algorithms. Then, these concepts are generalized to the algebraic context of semirings. Methods for creating new semirings, useful for modeling new problems, are provided. A large part of the book is then devoted to numerous applications of the algebraic path problem, ranging from mobile network routing to BGP routing to social networks. These applications show what kind of problems can be modeled as algebraic path problems; they also serve as examples on how to go about modeling new problems. This monograph will be useful to network researchers, engineers, and graduate students. It can be used either as an introduction to the topic, or as a quick reference to the theoretical facts, algorithms, and application examples. The theoretical background assumed for the reader is that of a graduate or advanced undergraduate student in computer science or engineering. Some familiarity with algebra and algorithms is helpful, but not necessary. Algebra, in particular, is used as a convenient and concise language to describe problems that are essentially combinatorial. Table of Contents: Classical Shortest Path / The Algebraic Path Problem / Properties and Computation of Solutions / Applications / Related Areas / List of Semirings and Applications
| Author | : John Baras |
| Publisher | : Springer Nature |
| Total Pages | : 65 |
| Release | : 2022-06-01 |
| Genre | : Computers |
| ISBN | : 3031799836 |
The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path problem, and an exposition of a broad range of applications. First of all, the shortest path problem is presented so as to fix terminology and concepts: existence and uniqueness of solutions, robustness to parameter changes, and centralized and distributed computation algorithms. Then, these concepts are generalized to the algebraic context of semirings. Methods for creating new semirings, useful for modeling new problems, are provided. A large part of the book is then devoted to numerous applications of the algebraic path problem, ranging from mobile network routing to BGP routing to social networks. These applications show what kind of problems can be modeled as algebraic path problems; they also serve as examples on how to go about modeling new problems. This monograph will be useful to network researchers, engineers, and graduate students. It can be used either as an introduction to the topic, or as a quick reference to the theoretical facts, algorithms, and application examples. The theoretical background assumed for the reader is that of a graduate or advanced undergraduate student in computer science or engineering. Some familiarity with algebra and algorithms is helpful, but not necessary. Algebra, in particular, is used as a convenient and concise language to describe problems that are essentially combinatorial. Table of Contents: Classical Shortest Path / The Algebraic Path Problem / Properties and Computation of Solutions / Applications / Related Areas / List of Semirings and Applications
| Author | : Guy Desaulniers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 369 |
| Release | : 2006-03-20 |
| Genre | : Business & Economics |
| ISBN | : 0387254862 |
Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
| Author | : Alex Fornito |
| Publisher | : Academic Press |
| Total Pages | : 496 |
| Release | : 2016-03-04 |
| Genre | : Medical |
| ISBN | : 0124081185 |
Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems - Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience - Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain
| Author | : Mourad Baïou |
| Publisher | : Springer Nature |
| Total Pages | : 302 |
| Release | : 2020-07-22 |
| Genre | : Computers |
| ISBN | : 3030532623 |
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Symposium on Combinatorial Optimization, ISCO 2020, which was due to be held in Montreal, Canada, in May 2020. The conference was held virtually due to the COVID-19 pandemic. The 24 revised full papers presented in this book were carefully reviewed and selected from 66 submissions.They were organized in the following topical sections: polyhedral combinatorics; integer programming; scheduling; matching; Network Design; Heuristics.
| Author | : Panos M. Pardalos |
| Publisher | : Springer |
| Total Pages | : 469 |
| Release | : 2011-04-21 |
| Genre | : Computers |
| ISBN | : 364220662X |
This volume constitutes the refereed proceedings of the 10th International Symposium on Experimental Algorithms, SEA 2011, held in Kolimpari, Chania, Crete, Greece, in May 2011. The 36 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 83 submissions and present current research in the area of design, analysis, and experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications.
| Author | : Ramesh Bhandari |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 1999 |
| Genre | : Computers |
| ISBN | : 9780792383819 |
Survivable Networks: Algorithms for Diverse Routing provides algorithms for diverse routing to enhance the survivability of a network. It considers the common mesh-type network and describes in detail the construction of physically disjoint paths algorithms for diverse routing. The algorithms are developed in a systematic manner, starting with shortest path algorithms appropriate for disjoint paths construction. Key features of the algorithms are optimality and simplicity. Although the algorithms have been developed for survivability of communication networks, they are in a generic form, and thus applicable in other scientific and technical disciplines to problems that can be modeled as a network. A notable highlight of this book is the consideration of real-life telecommunication networks in detail. Such networks are described not only by nodes and links, but also by the actual physical elements, called span nodes and spans. The sharing of spans (the actual physical links) by the network (logical) links complicates the network, requiring new algorithms. This book is the first one to provide algorithms for such networks. Survivable Networks: Algorithms for Diverse Routing is a comprehensive work on physically disjoint paths algorithms. It is an invaluable resource and reference for practicing network designers and planners, researchers, professionals, instructors, students, and others working in computer networking, telecommunications, and related fields.
| Author | : Catherine C. McGeoch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 371 |
| Release | : 2008-05-08 |
| Genre | : Computers |
| ISBN | : 3540685480 |
This book constitutes the refereed proceedings of the 7th International Workshop on Experimental and Efficient Algorithms, WEA 2008, held in Provincetown, MA, USA, in May/June 2008. The 26 revised full papers were carefully reviewed and selected from numerous submissions and present current research on experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications. Special focus is put on the use of experimental methods to guide the design, analysis, implementation, and evaluation of algorithms, heuristics, and optimization programs.
| Author | : Eiji Oki |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2012-08-24 |
| Genre | : Computers |
| ISBN | : 1466552646 |
Explaining how to apply to mathematical programming to network design and control, Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to m
| Author | : Ding-Zhu Du |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 395 |
| Release | : 2006-08-18 |
| Genre | : Business & Economics |
| ISBN | : 0387238301 |
This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
