Mathematics and Its Applications

Algorithms for Processing Trees

By: Victor N. Kasyanov, Vladimir A. Evstigneev

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Hardcover | 31 August 2000

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452 Pages

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23.39 x 15.6 x 2.54

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In delivering lectures and writing books, we were most often forced to pay absolutely no attention to a great body of interesting results and useful algorithms appearing in numerous sources and occasionally encountered. It was absolutely that most of these re sults would finally be forgotten because it is impossible to run through the entire variety of sources where these materials could be published. Therefore, we decided to do what we can to correct this situation. We discussed this problem with Ershov and came to an idea to write an encyclopedia of algorithms on graphs focusing our main attention on the algorithms already used in programming and their generalizations or modifications. We thought that it is reasonable to group all graphs into certain classes and place the algo rithms developed for each class into a separate book. The existence of trees, i. e. , a class of graphs especially important for programming, also supported this decision. This monograph is the first but, as we hope, not the last book written as part of our project. It was preceded by two books "Algorithms on Trees" (1984) and "Algorithms of Processing of Trees" (1990) small editions of which were published at the Computer Center of the Siberian Division of the Russian Academy of Sciences. The books were distributed immediately and this made out our decision to prepare a combined mono graph on the basis of these books even stronger.

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Published: 11th October 2012

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Preface	p. ix
Basic Concepts and Algorithms	p. 1
Trees and Their Properties	p. 1
Introduction and Basic Definitions	p. 1
Representations of Trees	p. 18
Numbering and Calculation of Trees	p. 39
Bibliographical Notes	p. 46
References	p. 46
Computational Models. Complexity and Fundamental Algorithms	p. 49
Introduction: Algorithm Representation Language	p. 49
Depth-First and Breadth-First Traversals of Graphs and Trees	p. 61
Generation of Trees	p. 91
Bibliographical Notes	p. 112
References	p. 115
Spanning Trees	p. 121
The Problem of Finding the Optimal Spanning Tree	p. 121
Algorithms of Numbering of All Spanning Trees	p. 140
Search of Spanning Trees with Given Properties	p. 154
Bibliographical Notes	p. 159
References	p. 163
Translation and Transformation of Programs	p. 175
Structural Trees	p. 175
Introduction and Principal Definitions	p. 175
Hierarchical Representations of Regularizable CF-Graphs	p. 187
Hammock Representations of CF-Graphs	p. 198
Exposure of the Dominance Relation	p. 208
Bibliographical Notes	p. 215
References	p. 219
Isomorphism, Unification, and Term-Rewriting Systems	p. 223
Isomorphisms of Trees	p. 223
Problem of Unification	p. 240
Term-Rewriting Systems	p. 267
Bibliographical Notes	p. 283
References	p. 285
Syntax Trees	p. 293
Language Syntax and the Problem of Syntax Analysis	p. 293
Generative Grammars	p. 295
Syntax Analysis	p. 302
Translation and Constructors of Analyzers	p. 323
Bibliographical Notes	p. 333
References	p. 333
Search and Storage of Information	p. 337
Information Trees	p. 337
Balanced Trees	p. 337
Multidimensional Trees (k-d-Trees)	p. 364
Bibliographical Notes	p. 372
References	p. 372
Trees for Multilevel Memory	p. 375
B-Trees	p. 375
Generalizations of B-Trees	p. 385
Multidimensional B-Trees	p. 393
Multiattribute Trees	p. 406
Bibliographical Notes	p. 418
References	p. 419
Additional List of Literature	p. 423
Subject Index	p. 427
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Mathematics and Its Applications

Algorithms for Processing Trees

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Hardcover

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