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＜電子ブック＞
Sparsity : Graphs, Structures, and Algorithms / by Jaroslav Nešetřil, Patrice Ossona de Mendez
(Algorithms and Combinatorics. ISSN:21976783 ; 28)

版	1st ed. 2012.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2012
本文言語	英語
大きさ	XXIII, 459 p. 132 illus., 100 illus. in color : online resource
著者標目	*Nešetřil, Jaroslav author Ossona de Mendez, Patrice author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Mathematical logic LCSH:Algorithms FREE:Discrete Mathematics FREE:Discrete Mathematics in Computer Science FREE:Convex and Discrete Geometry FREE:Mathematical Logic and Foundations FREE:Algorithms
一般注記	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 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 Nešetřil 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 HTTP:URL=https://doi.org/10.1007/978-3-642-27875-4

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