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The graph isomorphism problem : its structural complexity

Author: Johannes Köbler; Uwe Schöning; Jacobo Torán
Publisher: Boston ; Berlin [u.a.] : Birkhäuser, 1993.
Series: Progress in theoretical computer science, 10.
Edition/Format:   Print book : EnglishView all editions and formats
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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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Johannes Köbler; Uwe Schöning; Jacobo Torán
ISBN: 0817636803 9780817636807 3764336803 9783764336806
OCLC Number: 246882287
Description: 160 S : graph. Darst.
Contents: 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.
Series Title: Progress in theoretical computer science, 10.
Responsibility: Johannes Köbler ; Uwe Schöning ; Jacobo Torán.
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