Stephen Hedetniemi's Books

Fundamentals of Domination in Graphs

By: Teresa W. Haynes,Stephen Hedetniemi,Peter Slater

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Fundamentals of Domination in Graphs

By: Teresa W. Haynes,Stephen Hedetniemi,Peter Slater

Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination.

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Page Count

465

Publisher

CRC Press

Published Date

ISBN 10

1482246589

ISBN 13

9781482246582

Domination in Graphs

Volume 2: Advanced Topics

By: TeresaW. Haynes

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Domination in Graphs

Volume 2: Advanced Topics

By: TeresaW. Haynes

Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.

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Page Count

519

Publisher

Routledge

Published Date

ISBN 10

1351454641

ISBN 13

9781351454643

Domination in Graphs: Core Concepts

By: Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning

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Domination in Graphs: Core Concepts

By: Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning

This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they’ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.

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Page Count

655

Publisher

Springer Nature

Published Date

ISBN 10

3031094964

ISBN 13

9783031094965

Neural Network Design and the Complexity of Learning

By: J. Stephen Judd

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Neural Network Design and the Complexity of Learning

By: J. Stephen Judd

Using the tools of complexity theory, Stephen Judd develops a formal description of associative learning in connectionist networks. He rigorously exposes the computational difficulties in training neural networks and explores how certain design principles will or will not make the problems easier.Judd looks beyond the scope of any one particular learning rule, at a level above the details of neurons. There he finds new issues that arise when great numbers of neurons are employed and he offers fresh insights into design principles that could guide the construction of artificial and biological neural networks.The first part of the book describes the motivations and goals of the study and relates them to current scientific theory. It provides an overview of the major ideas, formulates the general learning problem with an eye to the computational complexity of the task, reviews current theory on learning, relates the book's model of learning to other models outside the connectionist paradigm, and sets out to examine scale-up issues in connectionist learning.Later chapters prove the intractability of the general case of memorizing in networks, elaborate on implications of this intractability and point out several corollaries applying to various special subcases. Judd refines the distinctive characteristics of the difficulties with families of shallow networks, addresses concerns about the ability of neural networks to generalize, and summarizes the results, implications, and possible extensions of the work. Neural Network Design and the Complexity of Learning is included in the Network Modeling and Connectionism series edited by Jeffrey Elman.

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Page Count

188

Publisher

MIT Press

Published Date

ISBN 10

0262100452

ISBN 13

9780262100458

Book's by Stephen Hedetniemi

Fundamentals of Domination in Graphs

Fundamentals of Domination in Graphs

Domination in Graphs

Domination in Graphs

Domination in Graphs: Core Concepts

Domination in Graphs: Core Concepts

Neural Network Design and the Complexity of Learning

Neural Network Design and the Complexity of Learning

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