The Graph Isomorphism Problem

1. Front Matter

   Pages i-vii

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2. Introduction

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 1-4

3. Preliminaries

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 5-10

4. Decision Problems, Search Problems, and Counting Problems

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 11-50

5. Quantifiers, Games, and Interactive Proofs

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 51-90

6. Circuits and Sparse Sets

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 91-116

7. Counting Properties

   • Johannes Köbler, Uwe Schöning, Jacobo Torán

   Pages 117-148

8. Back Matter

   Pages 149-160

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Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, and also, to give the reader an understanding of the aims and topics in Structural Complexity Theory, in general. The text is basically self contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. It can be used to teach a seminar or a monographic graduate course, but also parts of it (especially Chapter 1) provide a source of examples for a standard graduate course on Complexity Theory. Many people have helped us in different ways III the process of writing this book. Especially, we would like to thank V. Arvind, R.V. Book, E. May­ ordomo, and the referee who gave very constructive comments. This book project was especially made possible by a DAAD grant in the "Acciones In­ tegrada" program. The third author has been supported by the ESPRIT project ALCOM-II.

• NP
• NP-completeness
• Zero-Knowledge
• clsmbc
• complexity
• complexity theory
• linear optimization
• probability
• combinatorics
• algorithm analysis and problem complexity

• Abteilung Theoretische Informatik, Universität Ulm, Ulm, Germany

  Johannes Köbler

• Fakultät für Informatik, Universität Ulm, Ulm, Germany

  Uwe Schöning

• Dept. de Leng. i. Sist. Informatics, Universitat Politécnica de Catalunya, Barcelona, Spain

  Jacobo Torán

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