1st Edition

Mathematical and Algorithmic Foundations of the Internet

    222 Pages 74 B/W Illustrations
    by CRC Press

    221 Pages
    by CRC Press

    To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating their universality by presenting ideas and examples from various fields, including literature, history, and art.

    Progressing from fundamental concepts to more specific topics and applications, the text covers computational complexity and randomness, networks and graphs, parallel and distributed computing, and search engines. While the mathematical treatment is rigorous, it is presented at a level that can be grasped by readers with an elementary mathematical background. The authors also present a lighter side to this complex subject by illustrating how many of the mathematical concepts have counterparts in everyday life.

    The book provides in-depth coverage of the mathematical prerequisites and assembles a complete presentation of how computer networks function. It is a useful resource for anyone interested in the inner functioning, design, and organization of the Internet.

    An Unconventional Introduction to the Internet

    Exponential Growth

    Sequences and Trees
    The expressiveness of sequences
    Comparing sequences
    From sequences to trees

    The Algorithm: The Key Concept
    Functions, algorithms, and decidability
    Computational complexity
    Searching: a basic Internet problem
    Lower bounds
    A world of exponential problems
    Computation goes green

    A World of Randomness
    Probability theory develops
    Randomness as incompressibility
    Compressing and hashing
    Randomized algorithms
    Example: file sharing on the Internet
    Randomness and humans (instead of computers)

    Networks and Graphs
    The adjacency matrix and its powers
    The random growth of graphs
    Power laws: the rich get richer

    Giant Components, Small Worlds, Fat Tails, and the Internet
    The emergence of giant components
    The perception of small worlds
    Fat tails
    The DNS tree: between names and addresses
    The Internet graph
    The Web graph
    Graph communities and the Web

    Parallel and Distributed Computation
    The basic rules of cooperation
    Working in parallel: some logical problems
    A distributed world
    Some logically hard problems
    A closer look at routing

    Browsers and Search Engines
    Caching Web pages
    From browsers to search engines
    The anatomy of a search engine
    Spamming the Web

    From mail to telephones
    Storing information
    The hypertext revolution
    Where are we now, and where are we going?



    Fabrizio Luccio and Linda Pagli are professors of informatics at the University of Pisa.

    Graham Steel is an INRIA research fellow at LSV, CNRS & ENS de Cachan.

    … a succinct introduction to the technical side of the computational science that supports the internet. … The book’s prose is exceptional. The authors are clearly skilled communicators and have undertaken a substantial effort to make the text enjoyable. … a superb read for their targeted audience of curious people. … I would consider using this text in a first-year seminar within the undergraduate curriculum, a setting for which it seems perfectly well suited.
    —Allen G. Holder, INFORMS Journal on Computing, 2012

    This book is an interesting (and oddly charming) look at just a few of the interesting mathematical and algorithmic facets of the Internet and the Web. … I found it quite an enjoyable read—there were interesting viewpoints on several topics … . It was nice to read a technical book that combines fun and serious information.
    —Jeffrey Putnam, Computing Reviews, January 2012

    Overall, a good introduction to the logical problems of the Internet. Recommended.
    —P. Cull, CHOICE, December 2011

    Networks are everywhere in our lives from the Internet to biological, social and financial networks. The authors have provided a lively, masterful, but easy-to-read introduction to a complex subject by enriching mathematical concepts with delightful paradigms and historical material. A pleasure to read for all students.
    —Evangelos Kranakis, School of Computer Science, Carleton University, Ottawa, Ontario, Canada