Algorithms and Complexity

Algorithm Theory
Graduate Course - Winter Term 2020/21
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 Algorithms and Datastructures. Basic algorithms and data structures knowledge, comparable to what is done in Algorithms and Datastructures 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

Exam Information

  • Date and time. 22.03.2021, 9:00 - 11:00 am (2 hours). Please arrive by 8:45 am.
  • Mode. The exam will be written.
  • Location. Building 101 Room 00-026. Enter only after the student ID has been checked at the entrance.
  • Corona Information. Everyone has to wear a surgical mask or FFP2 mask (or equivalent) during the whole exam.
  • Allowed material. 5 A4 pages (corresponds to 5 singly-sided A4 sheets) of handwritten notes.
  • Preparation. Old exams are available further below.


Introductory Session: There will be an introductory event on Tuesday 3rd of November at 16:15 pm. It will take place via Zoom. The Zoom data is available here. Please consider the section below on technical information.

Lecture: The lecture will be given in a recorded form. Each week we will release a new video which you are supposed to watch. Click here for the videos and slides.

Exercises: There will be an exercise sheet every week which you should work on at home after watching the according lecture. The exercises will be published every Tuesday at 4 pm. They are due one week later (also at Tuesday 4 pm). Submission will be via Daphne. Please consider the section on technical information.

Exercise Classes: We will offer a weekly live session via Zoom where we discuss questions about the lecture and exercises. It will take place each Tuesday, 16:15 to 17:45. The Zoom data is available here. Please consider the section below on technical information.

Instant Messenger: We will offer an instant messaging platform (Zulip) for all students to discuss all topics related to this lecture, where you are free to discuss among yourself or pose questions to us. The Zulip data is available here. Please consider the section below on technical information.


Format: This semester we will only accept digital submissions! All submissions must be in, or converted to pdf format. We strongly recommend to prepare your solutions with Latex for best readability (being able to work with latex is a good skill to have anyway). Solutions prepared with Word or similar text editors are ok. Scans or photos of handwritten solutions in pdf format are ok as well, but must be well readable!

Submission Guidelines: The exercises will be conducted online with the course management system Daphne. The solution of each exercise must be uploaded to your SVN repository each one in a separate folder named exercise-XY, where XY is the exercise number (with a leading 0 if that number is smaller than 10). More on the submission via SVN in the technical information section.

Team Submission: Teams will be allowed. Teams may consist of at most three members! In case you submit your solution as part of a team, each team member must still submit a copy of the solution pdf to their respective SVN-repository (c.f. technical information). The members of the teams must be clearly marked on the top of the solution pdf.

Exercise sheet Assigned Due (4 pm) Solution

Exercise 01 (O-Notation, Divide & Conquer) 03.11.2020 10.11.2020 Solution 01
Exercise 02 (Divide & Conquer, FFT) 10.11.2020 17.11.2020 Solution 02
Exercise 03 (Greedy Algorithms) 17.11.2020 24.11.2020 Solution 03
Exercise 04 (Dynamic Programming) 24.11.2020 01.12.2020 Solution 04
Exercise 05 (Amortized Analysis, Union Find) 01.12.2020 08.12.2020 Solution 05
Exercise 06 (Fibonacci Heaps) 08.12.2020 15.12.2020 Solution 06
Exercise 07 (Max-Flow) 15.12.2020 22.12.2020 Solution 07
Exercise 08 (Vertex Cuts) 22.12.2020 12.01.2021 Solution 08
Exercise 09 (Matching, Randomization Part I) 12.01.2021 19.01.2021 Solution 09
Exercise 10 (Randomization Part II) 19.01.2021 26.01.2021 Solution 10
Exercise 11 (Randomization Part III) 26.01.2021 02.02.2021 Solution 11
Exercise 12 (Approximation Algorithms) 02.02.2021 09.02.2021 Solution 12
Exercise 13 (Online Algorithms) 09.02.2021 16.02.2021 Solution 13

Technical Information

Zoom and Zulip: All details for the weekly Zoom meeting are given on a seperate website. To join Zulip, click on the invitation link which is also given on this website.
Important note: This website can only be accessed from within the university network. This can be done by establishing a VPN tunnel to the university network.

Daphne: The exercises are submitted via Daphne. On Daphne, an overview of the points you achieved so far is given. Exercises are also available there. Please click on this link to register for the Algorithm Theory course with your rz-account.

Subversion (SVN): After registration, a SVN repository will be created for you with an URL of the following form:


You should do a "checkout" of your SVN-repository (using the URL described above) to get a local copy on your pc. With the command "update" you synchronize your local copy with the current version on the server. Through the command "commit" you upload your local files to your repository on the server. A more detailed overview can be found here. There are different subversion clients you can use. For Windows Tortoise-SVN is recommended.

Note that every solution of an exercise sheet must be uploaded ("committet") to a separate folder named exercise-XY, where XY is the exercise number (with a leading 0 if smaller than 10). This folder will be automatically locked (that is, no commits are possible anymore) after the submission deadline on the following Tuesday at 4 pm sharp!

Past Exams


  • 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