Sparsity : graphs, structures, and algorithms
 Author/Creator
 Nešetřil, Jaroslav.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2012.
 Physical description
 xxiii, 457 p. : ill. (some col.) ; 24 cm.
 Series
 Algorithms and combinatorics ; 28.
Access
Contributors
 Contributor
 Ossona de Mendez, Patrice.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 431450) and index.
 Contents

 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 TreeDepth. 8. Decomposition. 9. Independence. 10. FirstOrder 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 Nesetril 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Sparse matrices.
Bibliographic information
 Publication date
 2012
 Responsibility
 Jaroslav Nešetřil, Patrice Ossona de Mendez.
 Series
 Algorithms and combinatorics ; 28
 ISBN
 9783642278747
 3642278744
 9783642278754
 3642278752