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Descriptive complexity, canonisation, and definable graph structure theory

Author: Martin Grohe
Publisher: Cambridge Cambridge University Press 2017
Series: Lecture notes in logic, 47
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Martin Grohe
ISBN: 9781139028868 1139028863 9781107014527 1107014522
OCLC Number: 1012745425
Notes: Title from publisher's bibliographic system (viewed on 30 Aug 2017)
Description: 1 Online-Ressource (ix, 543 Seiten) PDF file(Seiten)
Contents: 1. Introduction; Part I. The Basic Theory: 2. Background from graph theory and logic; 3. Descriptive complexity; 4. Treelike decompositions; 5. Definable decompositions; 6. Graphs of bounded tree width; 7. Ordered treelike decompositions; 8. 3-Connected components; 9. Graphs embeddable in a surface; Part II. Definable Decompositions of Graphs with Excluded Minors: 10. Quasi-4-connected components; 11. K5-minor free graphs; 12. Completions of pre-decompositions; 13. Almost planar graphs; 14. Almost planar completions; 15. Almost embeddable graphs; 16. Decompositions of almost embeddable graphs; 17. Graphs with excluded minors; 18. Bits and pieces; Appendix. Robertson and Seymour's version of the local structure theorem; References; Symbol index; Index.
Series Title: Lecture notes in logic, 47
Responsibility: Martin Grohe

Abstract:

This groundbreaking, yet accessible book contains original results on the interaction between graph theory and computational complexity using methods from finite model theory. As well as a wealth of  Read more...

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'The book is divided evenly into two parts. Part I gives background and definitions of the main notions, and makes the book self-contained. Many results from descriptive complexity theory, and the Read more...

 
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