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Geometric Approximation Algorithms

Sariel Har-Peled University of Illinois at Urbana-Champaign, Urbana, IL
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Hardcover ISBN: 978-0-8218-4911-8
Product Code: SURV/173
List Price: $110.00 MAA Member Price:$99.00
AMS Member Price: $88.00 Electronic ISBN: 978-1-4704-1400-9 Product Code: SURV/173.E List Price:$103.00
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List Price: $165.00 MAA Member Price:$148.50
AMS Member Price: $132.00 Click above image for expanded view Geometric Approximation Algorithms Sariel Har-Peled University of Illinois at Urbana-Champaign, Urbana, IL Available Formats:  Hardcover ISBN: 978-0-8218-4911-8 Product Code: SURV/173  List Price:$110.00 MAA Member Price: $99.00 AMS Member Price:$88.00
 Electronic ISBN: 978-1-4704-1400-9 Product Code: SURV/173.E
 List Price: $103.00 MAA Member Price:$92.70 AMS Member Price: $82.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$165.00 MAA Member Price: $148.50 AMS Member Price:$132.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1732011; 362 pp
MSC: Primary 68; Secondary 52;

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.

Graduate students and research mathematicians interested in the theory and practice of computational geometry.

• Chapters
• 1. The power of grids—closest pair and smallest enclosing disk
• 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

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Volume: 1732011; 362 pp
MSC: Primary 68; Secondary 52;

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.

Graduate students and research mathematicians interested in the theory and practice of computational geometry.

• Chapters
• 1. The power of grids—closest pair and smallest enclosing disk
• 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
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