Course Description

This course is an introduction to the use of probability and randomization in computing. The use of probability in computing can be classified into roughly two classes, randomized algorithms, and probabilistic analysis. This course will introduce both techniques.

Some algorithms make a randomized decision (by "flipping a few coins") to decide what step to take next. Such algorithms are called randomized algorithms, and are pervasive within computing. Many of the most efficient algorithms for fundamental problems are randomized algorithms. In some cases, probability is used as a tool in analyzing the efficiency of algorithms and computer processes. In these cases, the input is modeled by a probability distribution, and this information is used in predicting the behavior of the algorithm. This is commonly referred to as probabilistic analysis. 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
• Sorting and finding Quantiles
• Hashing and Pattern Matching
• Distributed Systems
• Data Stream Processing
• Web Page Ranking
• Random Graph Models
• Network Traffic Data Analysis

Textbooks

• The textbook for the course 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

Schedule

Homeworks

1. Homework 1 (due Jan 31)
2. Homework 2 (due Feb 9)
3. Homework 3 (due Feb 21). Look here for datasets.
4. Homework 4 (due Apr 5)

Course Policies

Disability

Academic Integrity

Assorted Links

• Wikipedia has a nice description of the Bloom Filter
• Wikipedia on Random Number Generation
• Random.org - Random Number Generation Service
• Simulation of the Coupon Collector's Problem
• Information about the Monty Hall Game.
• 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.
• Consistent Hashing:
  • Wikipedia's take
  • Web Caching with Consistent Hashing
  • Consistent hashing and random trees: distributed caching protocols for relieving hot spots on the World Wide Web
• The PageRank Citation Ranking: Bringing Order to the Web
• Authoritative sources in a hyperlinked environment
• The space complexity of approximating the frequency moments