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Geometric Approximation Algorithms
About this Title
Sariel Har-Peled, University of Illinois at Urbana-Champaign, Urbana, IL
Publication: Mathematical Surveys and Monographs
Publication Year:
2011; Volume 173
ISBNs: 978-0-8218-4911-8 (print); 978-1-4704-1400-9 (online)
DOI: https://doi.org/10.1090/surv/173
MathSciNet review: 2760023
MSC: Primary 68U05; Secondary 52B55, 52C07, 68P05, 68W25
Table of Contents
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Front/Back Matter
Chapters
- 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 $\varepsilon$-nets and $\varepsilon$-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