TY  - BOOK
AU  - Sariel Har-Peled 
TI  - Geometric approximation algorithms
T2  - Mathematical Surveys and Monographs
SN  - 978-0-8218-4911-8
AV  - QA448.D38 
PY  - 2011///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - 1. The power of grids—closest pair and smallest enclosing disk
2. Quadtrees—hierarchical grids
3. Well-separated pair decomposition
4. Clustering—definitions and basic algorithms
5. On complexity, sampling, and ε-nets and ε-samples
6. Approximation via reweighting
7. Yet even more on sampling
8. Sampling and the moments technique
9. Depth estimation via sampling
10. Approximating the depth via sampling and emptiness
11. Random partition via shifting
12. Good triangulations and meshing
13. Approximating the Euclidean traveling salesman problem (TSP)
14. Approximating the Euclidean TSP using bridges
15. Linear programming in low dimensions
16. Polyhedrons, polytopes, and linear programming
17. Approximate nearest neighbor search in low dimension
18. Approximate nearest neighbor via point-location
19. Dimension Reducation - The Johnson-Lindenstrauss (JL)lemma
20. Approximate nearest neighbor (ANN) search in high dimensions
21. Approximating a convex body by an ellipsoid
22. Approximating the minimum volume bounding box of a point set
23. Coresets
24. Approximation using shell sets
25. Duality
26. Finite metric spaces and partitions
27. Some probability and tail inequalities
28. Miscellaneous prerequisite

N2  - Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts.

This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas. --- summary provided by publisher
ER  -