Download or read book Domination in Graphs written by TeresaW. Haynes and published by Routledge. This book was released on 2017-11-22 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""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.
Download or read book Dominating Sets in Planar Graphs written by Princeton University. Dept. of Computer Science and published by . This book was released on 1994 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallest [epsilon] such that, for n sufficiently large, every n-vertex planar graph contains a dominating set of size at most [epsilon]n. We prove that 1/4 [
Download or read book Dominating Sets in Planar Graphs written by Fedor V. Fomin and published by . This book was released on 2003 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Total Domination in Graphs written by Michael A. Henning and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is an excellent resource for students interested in beginning their research in this field. Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems.
Download or read book Connected Dominating Set Theory and Applications written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, especially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. In this book, we are going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets. The book consists of 16 chapters. Except the 1st one, each chapter is devoted to one problem, and consists of three parts, motivation and overview, problem complexity analysis, and approximation algorithm designs, which will lead the reader to see clearly about the background, formulation, existing important research results, and open problems. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics.
Download or read book Planar Graphs written by Takao Nishizeki and published by Courier Corporation. This book was released on 2008-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text features most of the important theorems and algorithms for planar graphs. Suitable as a textbook, it is also useful for researchers and includes an extensive reference section. 1988 edition.
Download or read book Computational Study for Domination Problems in Planar Graphs written by Marjan Marzban and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DOMINATING SET problem is one of the most widely studied problems in graph theory and networking. For a graph G(V, E), D [subset] V (G) is a dominating set of G if each vertex v of G is either in D or has a neighbour in D. Finding a minimum dominating set for arbitrary graphs is NP-hard and remains NP-hard for planar graphs. Recently, based on the notion of branch-decompositions, there has been significant theoretical progress towards fixed-parameter algorithms and polynomial time approximation schemes (PTAS) for the problem in planar graphs. However, little is known on the practical performances of those algorithms and a major hurdle for such evaluations is lack of efficient tools for computing branch-decompositions of input graphs. We develop efficient implementations of algorithms for computing optimal branch-decompositions of planar graphs. Based on these tools, we perform computational studies on a fixed-parameter exact algorithm and a PTAS for the DOMINATING SET problem in planar graphs. Our studies show that the fixed parameter exact algorithm is practical for graphs with small branchwidth and the PTAS is an efficient alternative for graphs with large branchwidth. We also perform analytical and computational studies for a branch-decomposition based fixed parameter exact algorithm for the CONNECTED DOMINATING SET (CDS) problem in planar graphs. We prove a better upper bound for the branchwidth in terms of the minimum size of CDS. Using this improved upper bound, we achieve an improved time complexity for the exact algorithm for the CDS problem. Finally, we show that the density of the CDS problem in planar graphs is 1/√5 in bidimensionality theorem.
Download or read book Complexity and Approximation written by Giorgio Ausiello and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.
Download or read book Fundamentals of Domination in Graphs written by Teresa W. Haynes and published by CRC Press. This book was released on 2013-12-16 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book Graphs Digraphs Fourth Edition written by Gary Chartrand and published by Chapman and Hall/CRC. This book was released on 1996-08-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third edition of the popular text on graph theory. As in previous editions, the text presents graph theory as a mathematical discipline and emphasizes clear exposition and well-written proofs. New in this edition are expanded treatments of graph decomposition and external graph theory, a study of graph vulnerability and domination, and introductions to voltage graphs, graph labelings, and the probabilistic method in graph theory.
Download or read book Exact Exponential Algorithms written by Fedor V. Fomin and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.
Download or read book Structures of Domination in Graphs written by Teresa W. Haynes and published by Springer Nature. This book was released on 2021-05-04 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.
Download or read book Sparsity written by Jaroslav Nešetřil and published by Springer Science & Business Media. This book was released on 2012-04-24 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.
Download or read book Distances and Domination in Graphs written by Ismael González Yero and published by MDPI. This book was released on 2020-11-18 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present.
Download or read book Fundamentals of Domination in Graphs written by Teresa W. Haynes and published by CRC Press. This book was released on 1998-01-05 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book Encyclopedia of Algorithms written by Ming-Yang Kao and published by Springer Science & Business Media. This book was released on 2008-08-06 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.
Download or read book Graph Theoretic Concepts in Computer Science written by Luděk Kučera and published by Springer Science & Business Media. This book was released on 2002-12-13 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002, held in Cesky Krumlov, Czech Republic in June 2002. The 36 revised full papers presented were carefully selected from initially 61 submissions during two rounds of reviewing and improvement. The papers provide a wealth of new results for various classes of graphs, graph computations, graph algorithms, and graph-theoretical applications in various fields.
