Mathematical and Algorithmic Foundations of the Internet  book cover
1st Edition

Mathematical and Algorithmic Foundations of the Internet

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ISBN 9781439831380
Published July 6, 2011 by CRC Press
221 Pages 74 B/W Illustrations

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Book Description

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.

Table of Contents

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?


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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