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The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has a comprehensive literature. A compelling element has been the threshold function, a short range in which events rapidly move from almost certainly false to almost certainly true. This book now joins the study of random graphs (and other random discrete objects) with mathematical logic. The possible threshold phenomena are studied for all statements expressible in a given language. Often there is a zero-one law, that every statement holds with probability near zero or near one. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures. The book will be of interest to graduate students and researchers in discrete mathematics.

Discrete mathematics --- Random graphs --- Logic, Symbolic and mathematical --- Graphes aléatoires --- Logique symbolique et mathématique --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical. --- Random graphs. --- Graphes aléatoires --- Logique symbolique et mathématique --- Graphes, Théorie des. --- Graphes aléatoires. --- Graph theory --- Discrete mathematics. --- Combinatorics. --- Computers. --- Computer science—Mathematics. --- Discrete Mathematics. --- Theory of Computation. --- Mathematics of Computing. --- 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 --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Graphes, Théorie des --- Graph theory. --- Logique mathematique --- Logique du premier ordre

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Graph drawing comprises all aspects of visualizing structural relations between objects. The range of topics dealt with extends from graph theory, graph algorithms, geometry, and topology to visual languages, visual perception, and information visualization, and to computer-human interaction and graphics design. This monograph gives a systematic overview of graph drawing and introduces the reader gently to the state of the art in the area. The presentation concentrates on algorithmic aspects, with an emphasis on interesting visualization problems with elegant solutions. Much attention is paid to a uniform style of writing and presentation, consistent terminology, and complementary coverage of the relevant issues throughout the 10 chapters. This tutorial is ideally suited as an introduction for newcomers to graph drawing. Ambitioned practitioners and researchers active in the area will find it a valuable source of reference and information.

Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer graphics --- Graph theory --- Technology - General --- Engineering & Applied Sciences --- Computer graphics. --- Graph theory. --- Graphs, Theory of --- Theory of graphs --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Extremal problems --- Mathematics. --- Information technology. --- Business --- Algorithms. --- Discrete mathematics. --- Combinatorics. --- Discrete Mathematics. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Computing. --- Computer Graphics. --- IT in Business. --- Data processing. --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Digital techniques --- Combinatorial analysis --- Topology --- Computer software. --- Computer science. --- IT (Information technology) --- Technology --- Telematics --- Information superhighway --- Knowledge management --- Combinatorics --- Algebra --- Mathematical analysis --- Informatics --- Science --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Business—Data processing. --- Algorism --- Arithmetic --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Foundations

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This book constitutes the joint refereed proceedings of the 4th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2001 and of the 5th International Workshop on Ranomization and Approximation Techniques in Computer Science, RANDOM 2001, held in Berkeley, California, USA in August 2001. The 26 revised full papers presented were carefully reviewed and selected from a total of 54 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization, de-randomization, average-case analysis, approximation classes, randomized complexity theory, scheduling, routing, coloring, partitioning, packing, covering, computational geometry, network design, and applications in various fields.

Computer science --- Computer Science --- Engineering & Applied Sciences --- Statistical methods --- Informatics --- Mathematics. --- Computer programming. --- Algorithms. --- Numerical analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Discrete mathematics. --- Combinatorics. --- Analysis. --- Programming Techniques. --- Discrete Mathematics. --- Algorithm Analysis and Problem Complexity. --- Numeric Computing. --- Science --- Global analysis (Mathematics). --- Computer science. --- Computer software. --- Electronic data processing. --- Combinatorics --- Algebra --- Mathematical analysis --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Software, Computer --- Computer systems --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Automation --- Algorism --- Arithmetic --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- 517.1 Mathematical analysis --- Foundations --- Programming --- Numerical Analysis.

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This volume contains the proceedings of the 22nd International Conference on Application and Theory of Petri Nets. The aim of the Petri net conferences is to create a forum for discussing progress in the application and theory of Petri nets. Typically, the conferences have 100{150 participants { one third of these coming from industry while the rest are from universities and research institutions. The conferences always take place in the last week of June. This year the conference was organized jointly with the 2nd International Conference on Application of Concurrency to System Design (ICACSD 2001). The two conferences shared the invited lectures and the social program. The conference and a number of other activities are co-ordinated by a steering committee with the following members: G. Balbo (Italy), J. Billington (Aust- lia), G. De Michelis (Italy), C. Girault (France), K. Jensen (Denmark), S. - magai (Japan), T. Murata (USA), C.A. Petri (Germany; honorary member), W. Reisig (Germany), G. Rozenberg (The Netherlands; chairman), and M. Silva (Spain). Other activities before and during the 2001 conference included tool dem- strations, a meeting on XML Based Interchange Formats for Petri Nets", - tensive introductory tutorials, two advanced tutorials on Probabilistic Methods in Concurrency" and Model Checking", and two workshops on Synthesis of Concurrent Systems" and Concurrency in Dependable Computing". The tu- rial notes and workshop proceedings are not published in these proceedings, but copies are available from the organizers.

Mathematics. --- Information technology. --- Business --- Computer communication systems. --- Software engineering. --- Mathematical logic. --- Computer science --- Mathematical Logic and Foundations. --- Software Engineering. --- Mathematical Logic and Formal Languages. --- Computer Communication Networks. --- Discrete Mathematics in Computer Science. --- IT in Business. --- Data processing. --- Petri nets --- Logic, Symbolic and mathematical. --- Computer science. --- Computational complexity. --- IT (Information technology) --- Technology --- Telematics --- Information superhighway --- Knowledge management --- Complexity, Computational --- Electronic data processing --- Machine theory --- Informatics --- Science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer software engineering --- Engineering --- Computer science—Mathematics. --- Business—Data processing. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Distributed processing --- Machine theory. --- Computer networks. --- Discrete mathematics. --- Business information services. --- Formal Languages and Automata Theory. --- Business enterprises --- Information services --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer mathematics --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics