CS 174
Randomized Algorithms Prof. Luca Trevisan
Spring 2003

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" 
Note: all problem sets and exams are offline
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 8.45  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 6.45  . 
17: March 20  Random walks III (Markov Chains)  MR 6.2  Homework 7 due
Homework 8 out 
March 2428  Spring break  
18: April 1  Random walks IV (Schoenig's algorithm)  LN9  . 
19: April 3
In 380 SODA 
Large deviation and routing  LN10, MR 4.12, 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, 13.13  Homework 9 due
Homework 10 out 
25: April 29  Fingerprints and polynomial identities  LN12, MR 7.12  . 
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
58pm 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 AgrawalBiswas probabilistic primality algorithm
(Lecture 27)
The AKS deterministic primality algorithm (Lecture 27)