The Graph Isomorphism Problem
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The Graph Isomorphism Problem: Its Structural Complexity

The Graph Isomorphism Problem: Its Structural Complexity

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About the Book

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.

Table of Contents:
Introduction Preliminaries Decision Problems, Search Problems, and Counting Problems NP-Completeness The Classes P and NP Reducibility. Reducing the Construction Problem to the Decision Problem Counting versus Deciding for Graph Isomorphism Uniqueness of the Solution Random Reductions Promise Problems Reducing Multiple Questions to One Quantifiers, Games, and Interactive Proofs The Polynomial-Time Hierarchy Interactive Proof Systems The Class IP Zero-Knowledge Probabilistic Classes Probability Amplification The BP-Operator Arthur-Merlin Games Lowness and Collapses Circuits and Sparse Sets Polynomial Size Circuits Circuits for NP Circuits for Graph Isomorphism Reductions to Sparse Sets Counting Properties Decision Reduces to Parity Graph Isomorphism is low for PP The Reconstruction Conjecture Bibliography Index


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Product Details
  • ISBN-13: 9783764336806
  • Publisher: Birkhauser Verlag AG
  • Publisher Imprint: Birkhauser Verlag AG
  • Height: 235 mm
  • Width: 155 mm
  • ISBN-10: 3764336803
  • Publisher Date: /05/1993
  • Binding: Hardback
  • Sub Title: Its Structural Complexity


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