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This clearly structured textbook/reference presents a detailed and comprehensive review of the fundamental principles of sequential graph algorithms, approaches for NP-hard graph problems, and approximation algorithms and heuristics for such problems. The work also provides a comparative analysis of sequential, parallel and distributed graph algorithms – including algorithms for big data – and an investigation into the conversion principles between the three algorithmic methods. Topics and features: Presents a comprehensive analysis of sequential graph algorithms Offers a unifying view by examining the same graph problem from each of the three paradigms of sequential, parallel and distributed algorithms Describes methods for the conversion between sequential, parallel and distributed graph algorithms Surveys methods for the analysis of large graphs and complex network applications Includes full implementation details for the problems presented throughout the text Provides additional supporting material at an accompanying website This practical guide to the design and analysis of graph algorithms is ideal for advanced and graduate students of computer science, electrical and electronic engineering, and bioinformatics. The material covered will also be of value to any researcher familiar with the basics of discrete mathematics, graph theory and algorithms. Dr. K. Erciyes is an emeritus professor of computer engineering at Ege University, Turkey. His other publications include the Springer titles Distributed Graph Algorithms for Computer Networks and Distributed and Sequential Algorithms for Bioinformatics.

Computer science. --- Algorithms. --- Computer science --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Mathematics. --- Computer software. --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Software, Computer --- Computer systems --- Graph algorithms. --- Discrete mathematics. --- Algorithms & data structures. --- Computer science—Mathematics. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer mathematics --- Mathematics

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This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups.  This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Number theory. --- Mathematics. --- Computer science --- Group theory. --- Combinatorics. --- Group Theory and Generalizations. --- Number Theory. --- Discrete Mathematics in Computer Science. --- Number study --- Numbers, Theory of --- Algebra --- Combinatorics --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Mathematics --- Computational complexity. --- Complexity, Computational --- Machine theory --- Computer science—Mathematics.

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This edited volume offers a detailed account on the theory of directed graphs from the perspective of important classes of digraphs, with each chapter written by experts on the topic. Outlining fundamental discoveries and new results obtained over recent years, this book provides a comprehensive overview of the latest research in the field. It covers core new results on each of the classes discussed, including chapters on tournaments, planar digraphs, acyclic digraphs, Euler digraphs, graph products, directed width parameters, and algorithms. Detailed indices ease navigation while more than 120 open problems and conjectures ensure that readers are immersed in all aspects of the field. Classes of Directed Graphs provides a valuable reference for graduate students and researchers in computer science, mathematics and operations research. As digraphs are an important modelling tool in other areas of research, this book will also be a useful resource to researchers working in bioinformatics, chemoinformatics, sociology, physics, medicine, etc.

Directed graphs. --- Mathematics. --- Algorithms. --- Computer science --- Graph theory. --- Graph Theory. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Digraphs (Graph theory) --- Oriented graphs --- Graph theory --- Computational complexity. --- Computer software. --- Software, Computer --- Computer systems --- Complexity, Computational --- Electronic data processing --- Machine theory --- Computer science—Mathematics. --- Algorism --- Algebra --- Arithmetic --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Foundations --- Extremal problems --- Discrete mathematics. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer mathematics --- Mathematics

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This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.

Rigidity (Geometry) --- Matrices. --- Geometric rigidity --- Rigidity theorem --- Discrete geometry --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Mathematical statistics. --- Discrete groups. --- Computational complexity. --- Statistical Theory and Methods. --- Convex and Discrete Geometry. --- Discrete Mathematics in Computer Science. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Groups, Discrete --- Infinite groups --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Discrete mathematics --- Statistics . --- Convex geometry . --- Discrete geometry. --- Computer science—Mathematics. --- Geometry --- Combinatorial geometry --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics

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This book constitutes the refereed post-conference proceedings of the First International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2017, held in Warsaw, Poland, in September 2017. The 15 revised full papers presented in this book together with 3 invited talks were carefully reviewed and selected from 32 initial submissions. The papers are organized in topical sections on elliptic curves in cryptography; public-key cryptography; lattices in cryptography; number theory; pseudorandomness; and algebraic structures and analysis.

Computer science. --- Software engineering. --- Data encryption (Computer science). --- Computer science --- Computers. --- Algorithms. --- Number theory. --- Computer Science. --- Data Encryption. --- Discrete Mathematics in Computer Science. --- Number Theory. --- Software Engineering/Programming and Operating Systems. --- Computing Milieux. --- Mathematics. --- Number study --- Numbers, Theory of --- Algebra --- Algorism --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Computer software engineering --- Engineering --- Informatics --- Science --- Foundations --- Mathematics --- Computational complexity. --- Cryptology. --- Complexity, Computational --- Computer science—Mathematics.