Patrice Ossona de Mendez: Sparsity

Cover: 9783642278747 | Sparsity | Graphs, Structures, and Algorithms | Mendez (u. a.) | Buch

Rückseite: 9783642278747 | Sparsity | Graphs, Structures, and Algorithms | Mendez (u. a.) | Buch

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Sprache: Englisch

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Beschreibung

This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants.
This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms.

Jaroslav Ne¿et¿il is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris.
This book is related to the material presented by the first author at ICM 2010.

Zusammenfassung

One of the first textbooks on the topic of sparsity - a core area of current discrete mathematics

Extremely useful to both mathematicians and computer scientists

Pedagogically excellent

Inhaltsverzeichnis

Part I Presentation: 1. Introduction.- 2. A Few Problems.- 3. Commented Contents.- Part II. The Theory: 4. Prolegomena.- 5. Measuring Sparsity.- 6. Classes and their Classification.- 7. Bounded Height Trees and Tree-Depth.- 8. Decomposition.- 9. Independence.- 10. First-Order Constraint Satisfaction Problems and Homomorphism Dualities.- 11. Restricted Homomorphism Dualities.- 12. Counting.- 13. Back to Classes.- Part III Applications: 14. Classes with Bounded Expansion - Examples.- 15. Property Testing, Hyperfiniteness and Separators.- 16. Algorithmic Applications.- 17. Other Applications.- 18. Conclusion.- Bibliography.- Index.- List of Symbols¿.

Erscheinungsjahr:	2012
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxiii 459 S. 32 s/w Illustr. 100 farbige Illustr. 459 p. 132 illus. 100 illus. in color.
ISBN-13:	9783642278747
ISBN-10:	3642278744
Sprache:	Englisch
Herstellernummer:	80114391
Einband:	Gebunden
Autor:	Ossona de Mendez, Patrice Ne¿et¿il, Jaroslav
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 32 mm
Von/Mit:	Patrice Ossona de Mendez (u. a.)
Erscheinungsdatum:	25.04.2012
Gewicht:	0,887 kg