Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Sparsity : graphs, structures, and algorithms / Jaroslav Nesetril and Patrice Ossona de Mendez.

By: Contributor(s): Material type: TextTextSeries: Algorithms and combinatorics ; 28.Publication details: Berlin : Springer-Verlag, 2012.Description: xxiii, 457 p. : ill. (some col.) ; 24 cmISBN:
  • 9783642278747 (hard cover : alk. paper)
Subject(s): DDC classification:
  • 511.6 23 N459
Contents:
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.
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.
Tags from this library: No tags from this library for this title. Log in to add tags.

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.

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in