Kirk Pruhs (He's the one on the left)

Phone : 412-624-8844 


Course Description

I will cover the basics of random processes and their analyses that arise frequently in CS related research, e.g.

Our primary goal is to learn the basics well, not to get to the frontier of research.

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.


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 2:30-3:45 in 5313 Sennott Square

Homework Groups

  1. Mohamed Aly, Christine Chung, Jonathan Misurda, Sherif Khattab Mahmoud Elhaddad
  2. Hammad Iobal, Ihsan Qazi, Dan Li, Xiuohui Kong








Wednesday January 4


Events and Probability

Verifying matrix multiplication


1.6 (Group B solution)

1.22 (Group A solution)

Monday January 9

2, 3


Moments and Deviations


Coupon Collector


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



Permutation Routing on n-Cube

4.9  (Group B solution)

4.25( Group A solution)

Monday Janurary 16

No Class, Martin Luther King Day


Wednesday January 18


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


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


 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

Notes by Alistair Sinclair

Wednesday February 15 8 Poisson Processes   8.8(Group A solution)

8.10(Group A solution)



Monday February 20 8 Queuing Theory M|M|1 and M|M|Infinity 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   Make-up 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: