Algorithms on trees and graphs : with python code
Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biolog...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Cham
Springer
2021
Springer International Publishing AG Springer International Publishing |
| Edition | 2 |
| Series | Texts in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783030818845 3030818845 |
| ISSN | 1868-0941 1868-095X |
| DOI | 10.1007/978-3-030-81885-2 |
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| Abstract | Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. Numerous illustrations, examples, and exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference |
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| AbstractList | Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. Numerous illustrations, examples, and exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference |
| Author | Valiente, Gabriel |
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| Copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 |
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| DOI | 10.1007/978-3-030-81885-2 |
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| EISBN | 3030818853 9783030818852 |
| EISSN | 1868-095X |
| Edition | 2 2nd ed. 2021 2nd ed. 2021. |
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| Publisher | Springer Springer International Publishing AG Springer International Publishing |
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| RelatedPersons | Hazzan, Orit Gries, David |
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| Snippet | Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial... |
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| SubjectTerms | Algorithms Computer Science Discrete Mathematics in Computer Science Graph algorithms Graph Theory Programming Languages, Compilers, Interpreters Python |
| TableOfContents | 7.4 Maximal Common Subgraph Isomorphism -- 7.4.1 An Algorithm for Maximal Common Subgraph Isomorphism -- 7.5 Applications -- A Implementation of the Algorithms in Python -- A.1 Introduction -- A.1.1 Basic Data Structures -- A.1.2 Representation of Trees and Graphs -- A.2 Algorithmic Techniques -- A.2.1 The Tree Edit Distance Problem -- A.2.2 Backtracking -- A.2.3 Branch-and-Bound -- A.2.4 Divide-and-Conquer -- A.2.5 Dynamic Programming -- A.3 Tree Traversal -- A.3.1 Preorder Traversal of a Tree -- A.3.2 Postorder Traversal of a Tree -- A.3.3 Top-Down Traversal of a Tree -- A.3.4 Bottom-Up Traversal of a Tree -- A.3.5 Applications -- A.4 Tree Isomorphism -- A.4.1 Tree Isomorphism -- A.4.2 Subtree Isomorphism -- A.4.3 Maximum Common Subtree Isomorphism -- A.5 Graph Traversal -- A.5.1 Depth-First Traversal of a Graph -- A.5.2 Breadth-First Traversal of a Graph -- A.5.3 Applications -- A.6 Clique, Independent Set, and Vertex Cover -- A.6.1 Cliques, Maximal Cliques, and Maximum Cliques -- A.6.2 Maximal and Maximum Independent Sets -- A.6.3 Minimal and Minimum Vertex Covers -- A.7 Graph Isomorphism -- A.7.1 Graph Isomorphism -- A.7.2 Graph Automorphism -- A.7.3 Subgraph Isomorphism -- A.7.4 Maximal Common Subgraph Isomorphism -- B Solutions to All Problems -- B.1 Introduction -- B.2 Algorithmic Techniques -- B.3 Tree Traversal -- B.4 Tree Isomorphism -- B.5 Graph Traversal -- B.6 Clique, Independent Set, and Vertex Cover -- B.7 Graph Isomorphism -- C Citing Publications -- Index Intro -- Preface to the Second Edition -- Preface to the First Edition -- References -- Contents -- blackPart I Introduction-1pt -- 1 Introduction -- 1.1 Trees and Graphs -- 1.2 Basic Data Structures -- 1.3 Representation of Trees and Graphs -- 2 Algorithmic Techniques -- 2.1 The Tree Edit Distance Problem -- 2.2 Backtracking -- 2.3 Branch-and-Bound -- 2.4 Divide-and-Conquer -- 2.5 Dynamic Programming -- blackPart II Algorithms on Trees-1pt -- 3 Tree Traversal -- 3.1 Preorder Traversal of a Tree -- 3.2 Postorder Traversal of a Tree -- 3.3 Top-Down Traversal of a Tree -- 3.4 Bottom-Up Traversal of a Tree -- 3.5 Applications -- 4 Tree Isomorphism -- 4.1 Tree Isomorphism -- 4.1.1 Ordered Tree Isomorphism -- 4.1.2 Unordered Tree Isomorphism -- 4.2 Subtree Isomorphism -- 4.2.1 Top-Down Subtree Isomorphism -- 4.2.2 Top-Down Unordered Subtree Isomorphism -- 4.2.3 Bottom-Up Subtree Isomorphism -- 4.2.4 Bottom-Up Unordered Subtree Isomorphism -- 4.3 Maximum Common Subtree Isomorphism -- 4.3.1 Top-Down Maximum Common Subtree Isomorphism -- 4.3.2 Top-Down Unordered Maximum Common Subtree Isomorphism -- 4.3.3 Bottom-Up Maximum Common Subtree Isomorphism -- 4.3.4 Bottom-Up Unordered Maximum Common Subtree Isomorphism -- 4.4 Applications -- blackPart III Algorithms on Graphs-1pt -- 5 Graph Traversal -- 5.1 Depth-First Traversal of a Graph -- 5.1.1 Leftmost Depth-First Traversal of a Graph -- 5.2 Breadth-First Traversal of a Graph -- 5.3 Applications -- 6 Clique, Independent Set, and Vertex Cover -- 6.1 Cliques, Maximal Cliques, and Maximum Cliques -- 6.2 Maximal and Maximum Independent Sets -- 6.3 Minimal and Minimum Vertex Covers -- 6.4 Applications -- 7 Graph Isomorphism -- 7.1 Graph Isomorphism -- 7.1.1 An Algorithm for Graph Isomorphism -- 7.2 Graph Automorphism -- 7.3 Subgraph Isomorphism -- 7.3.1 An Algorithm for Subgraph Isomorphism |
| Title | Algorithms on trees and graphs : with python code |
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