Fall 2010
Topics |
Date(s) |
Reading |
Randomized Algorithms, First Application: Contention Resolution in a Distributed System. Primitives of bounding probability of success/failure. Union Bound. Class Notes. |
Mon, Aug 23 |
Randomized Algorithms, Chapter 13 of "Algorithm Design" by Kleinberg and Tardos,
pages 707-713
and Class Notes. |
Randomized Algorithms, Second Application: Coupon Collection, a "high probability" bound. Primitives of bounding probability of success/failure (continued). Random Variables, Expectation, Linearity of Expectation. Class Notes. |
Wed, Aug 25 |
Randomized Algorithms, Chapter 13 of "Algorithm Design" by Kleinberg and Tardos,
paragraph 13.3, pages 719-724
and Class Notes. |
Randomized Algorithms, Second Application: Coupon Collection, in "Expectation" analysis. Random Variables, Expectation, Linearity of Expectation, Waiting for first Success. Class Notes. |
Fri, Aug 27 |
Randomized Algorithms, Chapter 13 of "Algorithm Design" by Kleinberg and Tardos,
paragraph 13.3, pages 719-724
and Class Notes. |
Mon, Aug 30 |
Randomized Algorithms, Chapter 13 of "Algorithm Design" by Kleinberg and Tardos,
paragraph 13.4, pages 724-727
and Class Notes. |
|
Review Homework 1
|
Wed, Sept 1 |
|
Finding a Global Min-Cut: Karger's Randomized Algorithm (Lecture by Prof. Eric Vigoda) |
Fri, Sept 3 |
Randomized Algorithms, Chapter 13 of "Algorithm Design" by Kleinberg and Tardos,
paragraph 13.4, pages 714-718
and Randomized Algorithms by Motwani and Raghavan, pages 7-10. |
Labor Day |
Mon, Sept 6 |
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Chernoff Bounds and Class Notes, Motivation and Theorems, Class Notes, Proof Skeleton Check Wikipedia for various forms of the bounds, and to see in details how Taylor Series give simpler expressions: http://en.wikipedia.org/wiki/Chernoff_bound, http://en.wikipedia.org/wiki/Taylor_series, http://en.wikipedia.org/wiki/Natural_logarithm, Application I: Estimating Ratios. |
Wed, Sept 8 |
(1)Class Notes, (2)Randomized Algorithms by Motwani and Raghavan, pages 67-72, (3)Notes by John Canny. |
Balancing Balls and Bins. ( Chernoff Bounds, Application II ) |
Fri, Sept 10 |
|
Set Balancing, aka Set Discrepancy (Class notes to be added). ( Chernoff Bounds, Application III ) |
Mon, Sept 13 |
(1)Class Notes (to be added) (2)Set Balancing, Motwani and Raghavan, Example 4.5, page 73. (3)Six Standard Deviations Suffice, by Joel Spencer, (in class we covered the notion of "realistic colorings"), (4)Raghavan's 1998 original paper. |
Simple randomized algorithms as starting points towards fundamentally new algorithmic techniques: Derandomization I: The Method of Conditional Probabilities (example: MAXKSAT) Pairwise Independence (example: MAX2SAT) |
Wed, Sept 15 |
(1)Class Notes (to be added), (2)Maximum Satisfiability, in Approximation Algorithms, by V. Vazirani, pages 131-134, (3)Pairwise Independence and Derandomization, by Luby and Widgerson. |
Review Homework 2
|
Fri, Sept 17 |
|
SAT versus MAXSAT (a detour in COMPLEXITY) (I) 2SAT is in P, a polynomial time algorithm for 2SAT MAX-2SAT is NP-hard, reduction fron 3SAT Class Notes. |
Mon, Sept 20 |
|
SAT versus MAXSAT (a detour in COMPLEXITY) (II) 2SAT is in P, a polynomial time algorithm for 2SAT MAX-2SAT is NP-hard, reduction fron 3SAT Class Notes. |
Wed, Sept 22 |