CS 174 Randomized Algorithms    Prof. Luca Trevisan     Spring 2003 Tuesdays and Thursdays, 3:30-5:00 pm 310 Soda

 randomization You that choose not by the view, Chance as fair and choose as true! Since this fortune falls to you, Be content and seek no new, (...) W. Shakespeare -- The Merchant of Venice derandomization Lisa: Where are the dice?  Todd: Daddy says dice are wicked.  Rod: We just move one space at a time. It's less fun that way   The Simpsons, Episode "My Sister, My Sitter"

### Work

Note: all problem sets and exams are off-line

• Exams
• Practice Midterm 1[Solutions]
• Midterm 1 (offline)  average 67, standard deviation 23.7
• Practice Midterm 2 [Solutions]
• Midterm 2 (offline)  average 54, standard deviation 15.8
You can pick up your midterm during Chris' office hours on Thursday 4-17.
• Practice Final (Solutions will be given in class May 8 and not posted on the web)
Final: May 13, 5-8pm, 10 Evans.

### Lectures

LN stands for lecture notes. MR stands for the textbook.

 Topic Readings Problem sets 1: January 21 Summary of the course LN0 . 2: January 23 Probability review; occupancy problems LN1 Homework 1 out 3: January 28 More occupancy problems LN1 . 4: January 30 Variance LN2, MR 3.2 Homework 1 due Homework 2 out 5: February 4 Random permutations LN2 6: February 6 Random permutations II LN3 Homework 2 due Homework 3 out 7: February 11 Random permutations III LN3 8: February 13 Karger's algorithm LN4, MR 1.1 Homework 3 due Homework 4 out 9: February 18 Random graphs LN4 . 10: February 20 Probabilistic method LN5 Homework 4 due February 25 MIDTERM I 11: February 27 Probabilistic method II LN5 Homework 5 out 12: March 4 Cliques in random graphs LN6 13: March 6 Hash Functions LN7, MR 8.4-5 Homework 5 due Homework 6 out 14: March 11 Skip Lists MR 8.3 . 15: March 13 Random walks LN8, MR 6.1, 6.3 Homework 6 due Homework 7 out 16: March 18 Random walks II LN8, MR 6.4-5 . 17: March 20 Random walks III (Markov Chains) MR 6.2 Homework 7 due Homework 8 out March 24-28 Spring break 18: April 1 Random walks IV (Schoenig's algorithm) LN9 . 19: April 3 In 380 SODA Large deviation and routing LN10, MR 4.1-2, 4.4 Homework 8 due 20: April 8 Entropy LN11 April 10 MIDTERM II 21: April 15 Entropy II LN11 22: April 17 Data Compression LN11 Homework 9 out. 23: April 22 Simulation of distributions 24: April 24 Byzantine Agreement, Paging MR 12.6, 13.1-3 Homework 9 due Homework 10 out 25: April 29 Fingerprints and polynomial identities LN12, MR 7.1-2 . 26: May 1 Pattern matching LN12, MR 7.6 Homework 10 due 27: May 6 Primality testing using polynomials LN13 28: May 8 Primality testing and Review LN13 May 13 5-8pm 10 Evans Final

Additional notes on probability from an old course.
The bible code. (Vaguely relates to Ramsey theory, lecture 10)
More on bloom filters. (Relates to hash functions, lecture 13)
Everything you wanted to know, and more, about hash functions from linear algebra (Lecture 13)
The original paper on Byzantine Agreement (Lecture 24)
The Agrawal-Biswas probabilistic primality algorithm (Lecture 27)
The AKS deterministic primality algorithm (Lecture 27)