The Graph Isomorphism Problem

Its Structural Complexity

J. Kobler, U. Schöning, J. Toran (Autoren)

Buch | Softcover

160 Seiten

2012 | Softcover reprint of the original 1st ed. 1993
Springer-Verlag New York Inc.
978-1-4612-6712-6 (ISBN)

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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.

Preliminaries.- 1 Decision Problems, Search Problems, and Counting Problems.- 1.1 NP-Completeness.- 1.2 Reducing the Construction Problem to the Decision Problem.- 1.3 Counting versus Deciding for Graph Isomorphism.- 1.4 Uniqueness of the Solution.- 1.5 Reducing Multiple Questions to One.- 2 Quantifiers, Games, and Interactive Proofs.- 2.1 The Polynomial-Time Hierarchy.- 2.2 Interactive Proof Systems.- 2.3 Probabilistic Classes.- 2.4 Lowness and Collapses.- 3 Circuits and Sparse Sets.- 3.1 Polynomial Size Circuits.- 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.

Reihe/Serie	Progress in Theoretical Computer Science
Zusatzinfo	VII, 160 p.
Verlagsort	New York
Sprache	englisch
Maße	210 x 279 mm
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4612-6712-9 / 1461267129
ISBN-13	978-1-4612-6712-6 / 9781461267126
Zustand	Neuware