##
Algorithm Theory

Graduate Course - Winter Term 2019/20

Fabian Kuhn

## Course Description

The design and analysis of algorithms is fundamental to computer science. In this course, we will study efficient algorithms for a variety of basic problems and, more generally, investigate advanced design and analysis techniques. Central topics are algorithms and data structures that go beyond what has been considered in the undergraduate course Informatik II. Basic algorithms and data structures knowledge, comparable to what is done in Informatik II is therefore assumed. The topics of the course include (but are not limited to):

- Divide and conquer: geometrical divide and conquer, fast fourier transformation
- Randomization: median, randomized quicksort, probabilistic primality testing
- Amortized analysis: Fibonacci heaps, union-find data structures
- Greedy algorithms: minimum spanning trees, scheduling, matroids
- Dynamic programming: matrix chain product problem, edit distance, longest common subsequence problem
- Graph algorithms: network flows, combinatorial optimization problems on graphs

## Schedule

The

**lecture**takes place each

**Thursday, 10:15 to 11:45 am**.

**There is no lecture on Thursday, 5th December. Instead, we ask you to watch the corresponding video of the 2017/18 lecture (see "Graph Algorithms - Part 2" on the slides and recordings page).**

On

**Tuesday, 4:15 to 5:45 pm**, there will be either a lecture or tutorial according to the following schedule:

14.01.20: Tutorial

21.01.20: Lecture

28.01.20: Tutorial

04.02.20: Lecture

11.02.20: Tutorial

#### Rooms:

Lecture: 101-00-026

German Tutorial (by Pascal Bachor): 101-00-026

English Tutorial (by Johannes Kalmbach): 101-01-016

## Exercises

Exercise sheet |
Due (10.15 am) |
Solution |
||

Exercise 01 (O-Notation, Divide & Conquer) | 31.10.2019 | Solution 01 | ||

Exercise 02 (FFT, Greedy) | 14.11.2019 | Solution 02 | ||

Exercise 03 (Dynamic Programming, Amortization) | 28.11.2019 | Solution 03 | ||

Exercise 04 (Data Structures) | 12.12.2019 | Solution 04 | ||

Exercise 05 (Maximum Flow and Applications) | 09.01.2020 | Solution 05 | ||

Exercise 06 (Randomization) | 23.01.2020 | Solution 06 | ||

Exercise 07 (Approximation) | 06.02.2020 | Solution 07 | ||

Exercise 08 (Online Algorithms) | Solution 08 |

#### Submission

You need to submit one solution per group (of at most two people). Submit your exercise solutions via one of the following options:

- Hand in as hard copy in lecture (before the deadline).
- Drop a hard copy into the Algorithm Theory [German/English] box in building 051.
- Send a digital version per mail to your tutor (click on the names below) with the subject 'AT_[SheeetNumber]'

With respect to digital submissions, we prefer solutions prepared with Latex, Word is ok, Scans must be well readable (no photos).

#### Grading

Your solutions will be graded by one of our tutors, Johannes Kalmbach (English tutorial) or Pascal Bachor (German tutorial). You can pick up your graded solutions during the next tutorial session.

Achieving 50% of the maximum achievable points on the exercise sheets is sufficient to be admitted to the exam.

## Lecture Material

All **slides and recordings** can be found on our Webserver.

Partly, the slides are modifications of earlier versions of
Prof. Dr. T. Ottmann and Prof. Dr. S. Albers.

## Forum

If you have a question to the lecture or the exercises, please
use the **forum** instead of writing an email. Then all of us and also your colleagues see the question and can answer to it. Feel free to also use the forum to discuss anything related to
the topics and organization of the lecture.

## Past Exams

- Algorithm Theory Exam Spring 2020
- Algorithm Theory Exam Spring 2019
- Algorithm Theory Exam Fall 2018
- Algorithm Theory Exam Spring 2018
- Algorithm Theory Exam Spring 2017
- Algorithm Theory Exam Fall 2016
- Algorithm Theory Exam Spring 2016
- Algorithm Theory Exam Fall 2015
- Algorithm Theory Exam Spring 2015
- Algorithm Theory Exam Fall 2014
- Algorithm Theory Exam Spring 2014
- Algorithm Theory Exam Fall 2013
- Algorithm Theory Exam Spring 2013

## Literature

- Jon Kleinberg and Éva Tardos: Algorithm Design, Addison Wesley
- Thomas H. Cormen, Charles E. Leiserson, Robert L. Rivest, and Cliford Stein: Introduction to Algorithms, MIT Press
- Thomas Ottmann and Peter Widmayer: Algorithmen und Datenstrukturen, Spektrum Akademischer Verlag