Download or read book Perfect Codes in General Graphs written by Jan Kratochvíl and published by . This book was released on 1991 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Codes and Decoding on General Graphs written by Niclas WIBERG and published by . This book was released on 1996 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parameterized and Exact Computation written by Dániel Marx and published by Springer. This book was released on 2012-03-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Symposium on Parameterized and Exact Computation, IPEC 2011, in Saarbrücken, Germany, in September 2011. The 21 revised full papers presented were carefully reviewed and selected from 40 submissions. The topics addressed cover research in all aspects of parameterized and exact computation and complexity, including but not limited to new techniques for the design and analysis of parameterized and exact algorithms, fixed-parameter tractability results, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized and exact computation, and implementation issues of parameterized and exact algorithms.
Download or read book Graphs Codes and Designs written by P. J. Cameron and published by Cambridge University Press. This book was released on 1980-07-31 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.
Download or read book Mathematical Foundations of Computer Science 1988 written by Michal P. Chytil and published by Springer Science & Business Media. This book was released on 1988-08-10 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 11 invited lectures and 42 communications presented at the 13th Conference on Mathematical Foundations of Computer Science, MFCS '88, held at Carlsbad, Czechoslovakia, August 29 - September 2, 1988. Most of the papers present material from the following four fields: - complexity theory, in particular structural complexity, - concurrency and parellelism, - formal language theory, - semantics. Other areas treated in the proceedings include functional programming, inductive syntactical synthesis, unification algorithms, relational databases and incremental attribute evaluation.
Download or read book Covering Codes written by G. Cohen and published by Elsevier. This book was released on 1997-04-14 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer. A number of unsolved problems suitable for research projects are also discussed.
Download or read book Connectivity domination and perfect codes in product graphs written by Simon Špacapan and published by . This book was released on 2007 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider several problems on the Cartesian, the direct and the strong product of graphs. We determine vertex connectivity of the Cartesian product and characterize minimum separating sets in the strong product of graphs. Edge connectivity for the strong product of graphs is determined as well. For the direct product of graphs we give sharp lower and upper bounds for the edge connectivity. We give necessary and sufficient conditions for existence of perfect codes in direct products of cycles and almost completely charactarize the existence of perfect codes in these graphs. Explicit construction of perfect codes in direct products of cycles is also provided. Broadcast domination is considered on all three graph products, where upper and lower bounds are obtained. Some exact values for the broadcast domination number of some classes of graphs are obtained. Optimal local structures in Cartesian products of cycles and tilings in a four-dimensional space (which are related to perfect Lee codes) are considered. Nonexistance theorems for optimal local structures and tilings are given. Total domination is also studied on direct products, where some bounds on this graph invariant are obtained.
Download or read book Perfect Codes And Related Structures written by Tuvi Etzion and published by World Scientific. This book was released on 2022-03-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes.The intention is to offer a different perspective for the area of perfect codes. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.The book can also be used as a textbook, either on basic course in combinatorial coding theory, or as an advance course in combinatorial coding theory.
Download or read book Random Graphs 87 written by Michal Karonski and published by . This book was released on 1990 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions to this volume are the proceedings of the Third International Seminar on Random Graphs and Probabilistic Methods in Combinatorics, a forum for this quickly growing area of research which combines discrete mathematics, probability theory and theoretical computer science. The papers from a team of international participants reflect the variety of topics in two areas. The first group of papers concern various properties of random graphs of different types such as random binomial graphs, regular and out-regular graphs, random mappings, trees and forests. The second group contribute to graph enumeration, percolation theory, the theory of parallel computation, statistical testing and the spread of information.
Download or read book Coding Theory and Design Theory written by Dijen Ray-Chaudhuri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".
Download or read book Fundamentals of Codes Graphs and Iterative Decoding written by Stephen B. Wicker and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.
Download or read book CMUC written by and published by . This book was released on 1989 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical and Engineering Methods in Computer Science written by Antonin Kucera and published by Springer. This book was released on 2013-01-17 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the post-proceedings of the 8th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, MEMICS 2012, held in Znojmo, Czech Republic, in October, 2012. The 13 thoroughly revised papers were carefully selected out of 31 submissions and are presented together with 6 invited papers. The topics covered by the papers include: computer-aided analysis and verification, applications of game theory in computer science, networks and security, modern trends of graph theory in computer science, electronic systems design and testing, and quantum information processing.
Download or read book Mathematical Foundations of Computer Science written by and published by . This book was released on 2004 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing and Combinatorics written by Bin Fu and published by Springer. This book was released on 2011-07-18 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th Annual International Conference on Computing and Combinatorics, held in Dallas, TX, USA, in August 2011. The 54 revised full papers presented were carefully reviewed and selected from 136 submissions. Topics covered are algorithms and data structures; algorithmic game theory and online algorithms; automata, languages, logic, and computability; combinatorics related to algorithms and complexity; complexity theory; computational learning theory and knowledge discovery; cryptography, reliability and security, and database theory; computational biology and bioinformatics; computational algebra, geometry, and number theory; graph drawing and information visualization; graph theory, communication networks, and optimization; parallel and distributed computing.
