Kirk Pruhs (He's the one on the left)
Email:
kirk@cs.pitt.edu
Phone : 4126248844
I will cover the basics of random processes and their analyses that arise frequently in CS related research, e.g.
Course Text
We will rather closely follow selected portions of the excellent text of Upfal and Mitzenmacher.
Course Format
We will cover essentially all of the excellent text of Upfal and Mitzenmacher. I will present all of these lectures. Each student may give one lecture at the end of the term on some paper from the area of random processes. I use the Socratic method, that is, I try to develop the ideas by asking the students leading questions. The grading will be based on a modest amount of daily homework and the final presentation.
Prerequisites
This is definitely not a pure algorithmics course. The graduate algorithms course is not a prerequisite. The prerequisite is familiarity with basic probability, e.g. random variables, expectations, conditional probability, etc., or the willingness to put more time in early in the course to catch up. Markov chains, Poisson processes etc. are widely used in many areas of CS, e.g. to model computing and communication systems. Having the ability to do basic analyses on such random processes will likely be an advantage to many of you in your research careers. So this course is intended for a broad range of students.
Class Time and Location
MW 2:303:45 in 5313 Sennott Square
Homework Groups
Schedule
Date 
Chapter 
Topic 
Applications 
Homework 
Wednesday January 4 
1 
Events and Probability 
Verifying matrix multiplication Mincut 
1.6 (Group B solution) 1.22 (Group A solution) 
Monday January 9 
2, 3 
Expectations Moments and Deviations

Coupon Collector Quicksort 
2.21 (Group A solution) 2.25 (Group B solution) 3.21 (A) 3.22(Group B solution)

Wednesday January 11 
3, 4 
Moments and Deviations Chernoff Bounds 
Searching Permutation Routing on nCube 
4.9 (Group B solution) 4.25( Group A solution) 
Monday Janurary 16 No Class, Martin Luther King Day 

Wednesday January 18 
5 
Balls and Bins 
Coupon Collector with Poisson Approximation 
5.10 (Group A solution) 5.11 (Group B solution) 
Monday January 23 No Class 




Wednesday January 25 
5 
Random Graphs 
Hamiltonian Cycle 
5.18 (Group B solution) 5.22 (Group A solution) 
Friday January 27 Special Class10:30am  SENSQ 5317 Distinguished Lecture by Sanjeev Arora





Monday January 28 
6 
Probabilistic Method 

6.2 (Group B solution) 6.8 (Group A solution) 
Wednesday January 30  6  Probabilistic Method 
6.14 (Group A solution) 6.16 (Group B solution) 

Monday February 6  6  Probabilistic Method  
Wednesday February 8  7 
Markov Chains Random Walks 
7.18 (Group A solution) 7.22 (B) 

Monday February 13  7 
Random Walks Relationship to Electrical Networks 

Wednesday February 15  8  Poisson Processes 
8.8(Group A solution) 8.10(Group A solution) 8.13(B) 8.23(B) 

Monday February 20  8  Queuing Theory  MM1 and MMInfinity Queues  
Wednesday February 22  9  Entropy 
9.12 (Group B
solution) 9.16 (A) 

Monday February 27  No Class  No Class  No Class  
Wednesday March 1  10  Monte Carlo Methods  
Monday March 13  10, 11  Monte Carlo Methods/Coupling 
10.6 (B) 10.10 (Group A solution) 

Wednesday March 15  11  Coupling 
11.7 (A)
11.16 (B) 

Monday March 20  12  Martingales  
Wednesday March 22  12  Martingales 
12.4 (A) 12.5 (B) 12.10 (B) 12.18 (A) 

Monday March 27  13  Pairwise Independence  
Wednesday March 29  13  Pairwise Independence  
Monday April 3  14  Balanced Allocations  
Wednesday April 5  14  Balanced Allocations  
Monday April 10  Christine Chung Presentation  
Wednesday April 12  Mohamed Aly Presentation  
Friday April 14  Mahmoud Elhaddad Presentation  
Monday April 17  Ihsan Qazi Presentation  
Wednesday April 19  Ziuohui Kong Presentation  
Friday April 21  Jonathan Misurda Presentation  
Monday April 24  Hammad Iobal Presentation  
Wednesday April 26  Dan Li Presentation  
Friday April 28  Makeup Presentation 
Research Papers
At the end of the semester, each student enrolled for a grade will present one paper from the recent theoretical computer science literature. Some possible papers (mostly from SODA 2005, STOC 2005, FOCS 2005, SODA 2006, STOC 2006) are listed below: