Pearls of Algorithms
Part 3: Probabilistic Analysis and Randomized Algorithms

General Information

What When Where Lecturer
Monday, 14:30 - 16:00
Wednesday, 8:15 - 9:45
HS III.03a / LBH
HS III.03a / LBH
Heiko Röglin
Wednesday, 12:30 - 14:00
Thursday, 12:30 - 14:00
LBH / II.57
LBH / II.57
Tobias Brunsch

Part 1 of this lecture was given by Norbert Blum.
Part 2 of this lecture was given by Rolf Klein.
Part 4 of this lecture was given by Marek Karpinski.


Date Contents Course Materials
December 9
1. Basic Probability Theory and Randomized Algorithms
1.1 Discrete Probability Spaces
1.2 Independent Events and Conditional Probability
Chapter 1 in [MU05]
December 11
1.3 Verifying Matrix Multiplication
1.4 Application: A Randomized Min-Cut Algorithm
Chapter 1 in [MU05]
December 16
1.4.1 Contract Algorithm
Chapter 1 in [MU05]
December 18
1.4.2 FastCut Algorithm
Chapter 10.2 in [MR95]
January 6
2. Smoothed Analysis
2.1 Introduction to Smoothed Analysis
January 8
2.2 Smoothed Analysis of the 2-Opt Algorithm for the TSP
January 13
2.3 Smoothed Analysis of the Knapsack Problem

Problem Sets


Students can take the oral exam with Professor Blum, Professor Karpinski, Professor Klein, or Professor Röglin. The exam will cover the whole semester, regardless of which examiner is chosen.

Exams with Heiko Röglin can be taken on February 10 and February 12. Re-exams will be on March 21. Students should send an email to Antje Bertram to schedule the exam.


There are lecture notes available for "2. Smoothed Analysis".

The following two books cover the topics discussed in "1. Basic Probability Theory and Randomized Algorithms". The Bachelor's course about randomized algorithms also covers some of the topics discussed in this class.