The Graph Isomorphism Problem

Its Structural Complexity

By: J. Kobler, U. Schöning, Jacobo Toran

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Hardcover | 1 July 1993

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172 Pages

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24.77 x 16.51 x 1.91

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The graph isomorphism problem belongs to the part of Complexity Theory that focuses on the structure of complexity classes involved in the classification of computational problems and in the relations among them. It consists in deciding whether two given graphs are isomorphic, i.e. whether there is a bijective mapping from the nodes of one graph to the nodes of the second graph such that the edge connections are respected. It is a problem of considerable practical as wen as theoretical importance that is, as of now, unresolved in the sense that no efficient algorithm for it has yet been found. Given this fact, it is natural to ask whether such an algorithm exists at an or whether the problem is intractable. -Be book focuses on this issue and presents several recent results that provide a better understanding of the relative position of the graph isomorphism problem in the class NP as well as in other complexity classes. It also uses the problem to illustrate important concepts in structural complexity, providing a look into the more general theory. 'The book is basically self-contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. Its level of presentation makes it eminently suitable for a seminar or graduate course devoted to the problem, or as a rich source of examples for a standard graduate course in Complexity Theory.

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You Can Find This Book In

Non-Fiction Mathematics Combinatorics & Graph Theory Applied Mathematics Computing & I.T.Computer Science Computer Architecture & Logic Design Databases Data Capture & Analysis Computer Programming & Software Development Algorithms & Data Structures Mathematical Theory of Computation

Maths for Computer Scientists

Introduction	p. 1
Preliminaries	p. 5
Decision Problems, Search Problems, and Counting Problems	p. 11
NP-Completeness	p. 12
Reducing the Construction Problem to the Decision Problem	p. 25
Counting versus Deciding for Graph Isomorphism	p. 30
Uniqueness of the Solution	p. 33
Reducing Multiple Questions to One	p. 44
Quantifiers, Games, and Interactive Proofs	p. 51
The Polynomial-Time Hierarchy	p. 52
Interactive Proof Systems	p. 58
Probabilistic Classes	p. 68
Lowness and Collapses	p. 84
Circuits and Sparse Sets	p. 91
Polynomial Size Circuits	p. 92
Reductions to Sparse Sets	p. 104
Counting Properties	p. 117
Decision Reduces to Parity	p. 118
Graph Isomorphism is Low for PP	p. 130
The Reconstruction Conjecture	p. 146
Bibliography	p. 149
Index	p. 158
Table of Contents provided by Blackwell. All Rights Reserved.

The Graph Isomorphism Problem

Its Structural Complexity

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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