Descriptive complexity, canonisation, and definable graph structure theory /:
Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book appro...
Gespeichert in:
| 1. Verfasser: | |
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| Körperschaft: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2017.
|
| Schriftenreihe: | Lecture notes in logic ;
47. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting. |
| Beschreibung: | 1 online resource (ix, 543 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139028868 1139028863 9781108234702 1108234704 |
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| 504 | |a Includes bibliographical references and index. | ||
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| contents | Introduction -- Background from graph theory and logic -- Descriptive complexity -- Treelike decompositions -- Definable decompositions -- Graphs of bounded tree width -- Ordered treelike decompositions -- 3-connected components -- Graphs embeddable in a surface -- Quasi-4-connected components -- K5-minor-free graphs -- Completions of pre-decompositions -- Almost planar completions -- Almost-embeddable graphs -- Decompositions of almost-embeddable graphs -- Graphs with excluded minors -- Bits and pieces. |
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| spelling | Grohe, M. (Martin), author. https://id.oclc.org/worldcat/entity/E39PBJgxmrM4WpCxPbHYkx4Xh3 http://id.loc.gov/authorities/names/no2006044149 Descriptive complexity, canonisation, and definable graph structure theory / Martin Grohe, Rheinisch-Westfä Cambridge : Cambridge University Press, 2017. 1 online resource (ix, 543 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture notes in logic ; 47 Online resource; title from PDF title page (EBSCO, viewed January 17, 2018) Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting. Includes bibliographical references and index. Introduction -- Background from graph theory and logic -- Descriptive complexity -- Treelike decompositions -- Definable decompositions -- Graphs of bounded tree width -- Ordered treelike decompositions -- 3-connected components -- Graphs embeddable in a surface -- Quasi-4-connected components -- K5-minor-free graphs -- Completions of pre-decompositions -- Almost planar completions -- Almost-embeddable graphs -- Decompositions of almost-embeddable graphs -- Graphs with excluded minors -- Bits and pieces. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 MATHEMATICS General. bisacsh Teoría de grafos embne Matemáticas embne Graph theory fast Association for Symbolic Logic. http://id.loc.gov/authorities/names/n50054564 has work: Descriptive complexity, canonisation, and definable graph structure theory (Text) https://id.oclc.org/worldcat/entity/E39PCGhJcJkvkQ98KFFcyppjJC https://id.oclc.org/worldcat/ontology/hasWork Lecture notes in logic ; 47. http://id.loc.gov/authorities/names/n93082404 |
| spellingShingle | Grohe, M. (Martin) Descriptive complexity, canonisation, and definable graph structure theory / Lecture notes in logic ; Introduction -- Background from graph theory and logic -- Descriptive complexity -- Treelike decompositions -- Definable decompositions -- Graphs of bounded tree width -- Ordered treelike decompositions -- 3-connected components -- Graphs embeddable in a surface -- Quasi-4-connected components -- K5-minor-free graphs -- Completions of pre-decompositions -- Almost planar completions -- Almost-embeddable graphs -- Decompositions of almost-embeddable graphs -- Graphs with excluded minors -- Bits and pieces. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 MATHEMATICS General. bisacsh Teoría de grafos embne Matemáticas embne Graph theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85056471 |
| title | Descriptive complexity, canonisation, and definable graph structure theory / |
| title_auth | Descriptive complexity, canonisation, and definable graph structure theory / |
| title_exact_search | Descriptive complexity, canonisation, and definable graph structure theory / |
| title_full | Descriptive complexity, canonisation, and definable graph structure theory / Martin Grohe, Rheinisch-Westfä |
| title_fullStr | Descriptive complexity, canonisation, and definable graph structure theory / Martin Grohe, Rheinisch-Westfä |
| title_full_unstemmed | Descriptive complexity, canonisation, and definable graph structure theory / Martin Grohe, Rheinisch-Westfä |
| title_short | Descriptive complexity, canonisation, and definable graph structure theory / |
| title_sort | descriptive complexity canonisation and definable graph structure theory |
| topic | Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 MATHEMATICS General. bisacsh Teoría de grafos embne Matemáticas embne Graph theory fast |
| topic_facet | Graph theory. MATHEMATICS General. Teoría de grafos Matemáticas Graph theory |
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