CprE 528x: Probabilistic Methods in Computer Engineering

CprE 528x: Probabilistic Methods in Computer Engineering
Fall 2008

Tue, Thu 11am - 12.20pm

Instructor: Srikanta Tirthapura
Email: snt@iastate.edu
Office: Room 3212, Coover Hall
Phone: (515) 294-3546
Office Hours: To be Announced

Syllabus	Course Schedule	Homeworks	Assignments
Textbooks	Grading	Course Policies	Links

Course Description

This course is an introduction to the use of probability and randomization in computing. Randomization is useful in a surprising number of applications, including network routing, computational biology, cryptography, processing massive data sets, etc. The course will begin by introducing a basic set of techniques for analyzing discrete random variables and probabilistic processes, and will demonstrate their use in a broad range of applications in computer engineering.

Tentative list of topics:

Basics of Discrete Random Variables, and their use in modeling algorithm behavior
Tail Inequalities for Sums of Independent Random Variables -- Markov, Chebyshev and Chernoff Bounds
Balls in Bins, Occupancy Problems
Random Graphs
Sorting and finding Quantiles
Randomized Data Structures
P2P Routing in Distributed Systems
Hashing and Pattern Matching
Aggregate Computation over Massive Data Streams
Graph Algorithms - Minimum Spanning Trees, Min Cut
Web Page Ranking

Textbooks

The textbook for the course (available at the bookstore) is Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher and Eli Upfal.

The following book is highly recommended: Randomized Algorithms by Rajeev Motwani and Prabhakar Raghavan.

Grading

The grading will be based on homeworks and assignments, and a class presentation.

Homeworks and Assignments: 60 %
Class Participation: 10 %
Project and Presentation: 30 %

Schedule

Day	Topic	Reading/Homeworks
Tue, Aug 26	First Class
Tue, Nov 25	Thanksgiving Break
Thu, Nov 27	Thanksgiving Break

Homeworks

coming up

Assignments

Course Policies

Disability

If you have a documented disability and anticipate needing accommodations in this course, please make arrangements to meet with me soon. Please request that a Disability Resources staff send a SAAR form verifying your disability and specifying the accommodations you will need.

Academic Integrity

All your work should be done individually unless otherwise specified. You are not allowed to use work done by others, or obtain the answers directly in any form (such as from the web). If you have any questions about what is allowed/not, please contact the instructor, and please refer to the university policies on academic dishonesty .

Assorted Links

Wikipedia on Random Number Generation

Random.org - Random Number Generation Service

Simulation of the Coupon Collector's Problem

Let's Make a Deal was a popular TV show where a participant can use her knowledge of probability to improve her chance of winning.

Buffon's Needle: An Analysis and Simulation is an interesting problem in continuous probability.

Java Demonstration of a Skip List.
A Skip list is a simple randomized alternative to Balanced Trees for Dynamic Dictionaries. The algorithms for the insertion and deletion from a skip list are quite simple, and "balance" is maintained through the use of randomization. Understanding the skip list can give a good insight into one way of using randomization in designing algorithms, and the analysis of such algorithms using the laws of probability.