Skip to Main Content
Theory of Computational Complexity, 2nd Edition
book

Theory of Computational Complexity, 2nd Edition

by Ding-Zhu Du, Ker-I Ko
June 2014
Intermediate to advanced content levelIntermediate to advanced
512 pages
17h 55m
English
Wiley
Content preview from Theory of Computational Complexity, 2nd Edition

Chapter 7

Polynomial-Time Isomorphism

Two decision problems are said to be polynomial-time isomorphic if there is a membership-preserving one-to-one correspondence between the instances of the two problems, which is both polynomial-time computable and polynomial-time invertible. Thus, this is a stronger notion than the notion of equivalence under the polynomial-time many-one reductions. It has, however, been observed that many reductions constructed between natural NP-complete problems are not only many-one reductions but can also be easily converted to polynomial-time isomorphisms. This observation leads to the question of whether two NP-complete problems must be polynomial-time isomorphic. Indeed, if this is the case then, within a polynomial factor, all NP-complete problems are actually identical and any heuristics for a single NP-complete problem works for all of them. In this chapter, we study this question and the related questions about the isomorphism of EXP-complete and P-complete problems.

7.1 Polynomial-Time Isomorphism

Let us start with a simple example.

Example 7.1

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Theory of Computation

Theory of Computation

George Tourlakis

Publisher Resources

ISBN: 9781118594971Purchase book