Algorithms and Complexity

Algorithm Theory
Graduate Course - Winter Term 2018/19
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, or , 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


Announcement: Due to the extended submission period for the 5th exercise sheet over the holidays, we shift our schedule by one week. Therefore, on Thursday the 10th of January 2019 the tutorials will take place (usual time and place).


  • Monday 14:15-16:00 Room: 101-00-026
  • Thursday 10:15-12:00 biweekly! Room: 101-00-026


  • English Tutorial (Johannes Kalmbach): Thursday 10:15-12:00 biweekly! Room: 101-00-026
  • German Tutorial (Pascal Bachor): Thursday 16:15-18:00 biweekly! Room: 51-00-034

Exercise Material

Exercise sheet Assigned Due (14.15 pm) Solution

Exercise 01 (O-Notation, Divide & Conquer) 22.10.2018 05.11.2018 Solution 01
Exercise 02 (Divide & Conquer, Greedy Algorithms) 05.11.2018 19.11.2018 Solution 02
Exercise 03 (Dyn. Programming, Amort. Analysis) 19.11.2018 03.12.2018 Solution 03
Exercise 04 (Data Structures,Graph Algorithms) 03.12.2018 17.12.2018
Exercise 05 (Matching, Probability Theory) 17.12.2018 07.01.2019
Exercise 06 (Randomization) 08.01.2019 21.01.2019


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).


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.


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.


  • 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