Lecture 16
- 1. Randomized Algorithms CS648 Lecture 16 Randomized Incremental Construction (Backward analysis) 1
- 4. A 1 2 … 4
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- 6. A 1 2 … 6
- 7. Fact: A is permuted randomly uniformly 7
- 8. A 1 2 … 8
- 9. PROBLEM 2 CLOSEST PAIR OF POINTS 9
- 10. Closest Pair of Points 10
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- 21. Randomized Incremental Construction • Convex Hull of a set of points • Trapezoidal decomposition of a set of segments. • Convex polytope of a set of half-planes • Smallest sphere enclosing a set of points. • Linear programming in finite dimensions. 21
- 22. PROBLEM 3 CONVEX HULL OF POINTS 22
- 23. Convex hull of Points 23
- 24. Convex hull of Points 24
- 25. Randomized algorithm for convex hull 25
- 26. A simple exercise from geometry Exercise: Given a line L and two points p and q, determine whether the points lie on the same/different sides of L. L p q q 26
- 27. Conflict graph : a powerful data structure cones 27
- 28. Before entering the for loop 28
- 29. Before entering the for loop cones 29
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- 32. cones 32
- 33. cones 33
- 34. cones 34
- 35. cones 35
- 36. cones 36
- 37. cones 37
- 38. cones 38
- 39. cones 39
- 40. cones 40
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- 46. Running time of the algorithm 46
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