TY  - BOOK
AU  - Nesetril,Jaroslav
AU  - Ossona de Mendez,Patrice
TI  - Sparsity: graphs, structures, and algorithms 
T2  - Algorithms and combinatorics
SN  - 9783642278747 (hard cover : alk. paper)
U1  - 511.6 23
PY  - 2012///
CY  - Berlin
PB  - Springer-Verlag
KW  - Combinatorial analysis
KW  - Sparse matrices
N1  - Includes bibliographical references and index; 1. Introduction --
2. A few problems --
3. Prolegomena --
4. Measuring sparsity --
5. Classes and their classification --
6. Bounded height trees and tree-depth --
7. Decomposition --
8. Independence --
9. First-order CSP, limits, and homomorphism dualities --
10. Preservation theorems --
11. Restricted homomorphism dualities --
12. Counting --
13. Back to classes --
14. Classes with bounded expansion --
15. Some applications --
16. Property testing, hyperfiniteness, and separators --
17. Core algorithms --
18. Algorithmic applications --
19. Further directions
N2  - 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.
ER  -