Mathematical and Algorithmic Foundations of the Internet: 1st Edition (Paperback) book cover

Mathematical and Algorithmic Foundations of the Internet

1st Edition

By Fabrizio Luccio, Linda Pagli, Graham Steel

CRC Press

221 pages | 74 B/W Illus.

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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.


… 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

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?


About the Authors

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.

About the Series

Chapman & Hall/CRC Applied Algorithms and Data Structures series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Programming / Algorithms
MATHEMATICS / Combinatorics