Jump to ContentJump to Main Navigation
The Nature of Computation$
Users without a subscription are not able to see the full content.

Cristopher Moore and Stephan Mertens

Print publication date: 2011

Print ISBN-13: 9780199233212

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199233212.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 03 December 2020

The Basics

The Basics

Chapter:
(p.15) Chapter 2 The Basics
Source:
The Nature of Computation
Author(s):

Cristopher Moore

Stephan Mertens

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199233212.003.0002

This chapter discusses the complexity of a problem by thinking about the best possible algorithm, or computer program, that solves it. It shows that computational complexity theory is not about how to write better programs, but about understanding the underlying structure of different problems as well as asking fundamental questions about them. The chapter first explains problems and solutions by considering a Eulerian path and a Hamiltonian path. It then examines Euclid's algorithm, time and space, and the notion of scaling in physics. It also analyzes the distinction between polynomial functions of n and exponential ones, why this distinction is very important, and why it is so robust with respect to changes in the definition of computation. Finally, the chapter looks at the tractability and mathematical insight into a problem's structure.

Keywords:   computational complexity theory, problems, solutions, Eulerian path, Hamiltonian path, Euclid's algorithm, time, space, scaling, polynomial functions

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .