Graph Isomorphism Problem : Its Structural Complexity

Kobler, J.; Schöning, U.; Toran, Jacobo

ISBN 10: 1461267129 / ISBN 13: 9781461267126

Editore: Birkhäuser, 2012

Codice articolo 19199673-n

Riassunto:

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.

Contenuti: Preliminaries.- 1 Decision Problems, Search Problems, and Counting Problems.- 1.1 NP-Completeness.- 1.1.1 The Classes P and NP.- 1.1.2 Reducibility.- 1.2 Reducing the Construction Problem to the Decision Problem.- 1.3 Counting versus Deciding for Graph Isomorphism.- 1.4 Uniqueness of the Solution.- 1.4.1 Random Reductions.- 1.4.2 Promise Problems.- 1.5 Reducing Multiple Questions to One.- 2 Quantifiers, Games, and Interactive Proofs.- 2.1 The Polynomial-Time Hierarchy.- 2.2 Interactive Proof Systems.- 2.2.1 The Class IP.- 2.2.2 Zero-Knowledge.- 2.3 Probabilistic Classes.- 2.3.1 Probability Amplification.- 2.3.2 The BP-Operator.- 2.3.3 Arthur-Merlin Games.- 2.4 Lowness and Collapses.- 3 Circuits and Sparse Sets.- 3.1 Polynomial Size Circuits.- 3.1.1 Circuits for NP.- 3.1.2 Circuits for Graph Isomorphism.- 3.2 Reductions to Sparse Sets.- 4 Counting Properties.- 4.1 Decision Reduces to Parity.- 4.2 Graph Isomorphism is Low for PP.- 4.3 The Reconstruction Conjecture.

Dati bibliografici

Titolo: Graph Isomorphism Problem : Its Structural ...
Casa editrice: Birkhäuser
Data di pubblicazione: 2012
Legatura: Brossura
Condizione: New