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Lecture 22-cs648
- 1. Randomized Algorithms CS648 Lecture 22 • Chebyshev Inequality • Method of Bounded Difference 1
- 3. THREE EXAMPLES TO ILLUSTRATE THE INAPPLICABILITY OF CHERNOFF BOUND 3
- 4. Red-blue balls out of bin 4
- 5. Balls into Bins (number of empty bins) 1 2 3 4 5 1 2 3 … … m-1 m … n 5
- 6. Number of Triangles in a random graph 6
- 10. METHOD OF BOUNDED DIFFERENCE (MOBD) The most powerful method for bounding the probability of deviation of a random variable from expected value 10
- 11. The Power of MOBD 11
- 12. Notations 12
- 13. A new perspective … The next slide will give a visual description of the process mentioned above. But ponder over this slide before pressing the next button. 13
- 14. … … … … … 14
- 15. … … … … … 15
- 16. … … … … … 16
- 18. Method of Bounded Difference … … … … … 18
- 19. Method of Bounded Difference … … … … … 19
- 20. Method of Bounded Difference - I … … … … … 20
- 21. Method of Bounded Difference - II 21
- 22. MOBD SUBSUMES CHERNOFF BOUND 22
- 23. MOBD subsumes Chernoff Bound 23
- 24. PROBLEM 1 NO. OF EMPTY BINS 24
- 25. Balls into Bins (number of empty bins) 1 2 3 4 5 1 2 3 … … n-1 n … n This will give very inferior bound 25
- 26. Balls into Bins (number of empty bins) 1 2 3 4 5 1 2 3 … … n-1 n … n 26
- 27. Balls into Bins (number of empty bins) 27
- 28. PROBLEM 2 RED-BLUE BALLS OUT OF BIN 28
- 29. Red-blue balls out of bin 29
- 30. Red-blue balls out of bin … … … 30
- 31. Red-blue balls out of bin 31
- 32. PROBLEM 3 NO. OF TRIANGLES IN RANDOM GRAPH Do it as exercise. This problem will also be posted in practice sheet. 32