Approximation Algorithms

Lecture: Tuesdays, 15:00-16:30, SN 19.2
Tutorial and Homework Discussion: Wednesday, 11:30-13:00, SN 19.4

Lecture: October, 29th; Tutorial: November, 13th; Homework Discussion: November, 20th

Prerequisites are knowledge of algorithms and data structures, basic graph problems and graph algorithms (e.g., as provided in the lecture "Netzwerkalgorithmen"); basic knowledge from theoretical computer science (NP-completeness) are helpful, but will definitely be supplemented.

Many interesting and natural algorithmic problems (e.g., the Traveling Salesman Problem) are NP-complete - hence, we cannot expect to find a "perfect" algorithm that (i) always and (ii) fast finds (iii) an optimal solution. However, hard problems still need to be solved!

In this class we consider algorithms that do not necessarily find an optimal solution, but that (i) always and (ii) fast find a (iii) provably good solution.

Among the topics of this class are:

1. A basic introduction to NP-completeness and approximation
2. Approximation for vertex and set cover
3. Packing problems
4. Tour problems and variations
5. Current research problems

In the context of various problems, a wide spectrum of techniques and concepts will be provided.

General Information

• We only use this website and the mailinglist mentioned below to distribute informations; the information on other sites such as StudIP etc. may be missing or outdated.
• If there are any questions, do not hesitate to write a mail.

Video recordings

The lectures are videotaped; videos will typically be published on this website the day after the lecture. The video is available as h264-encoded mp4 that should be supported by any reasonable video player, and a newer, better and smaller h265-encoded mkv which requires a relatively recent video player.

A note for Firefox users: Some versions of Firefox do not support playback of sound in the video due to the channel layout; if you do not have sound in the browser, just download the video and use a regular video player such as VLC or mplayer.

• Lecture 1: [mp4] [mkv]
• Lecture 2: [mp4] [mkv]
• Lecture 3: [mp4] [mkv]
• Lecture 4: [mp4] [mkv]
• Lecture 5: [mp4] [mkv]
• Lecture 6: [mp4] [mkv]
• Lecture 7: [mp4] [mkv]
• Lecture 8: [mp4] [mkv]
• Lecture 9: [mp4] [mkv]
• Lecture 10: [mp4] [mkv]
• Lecture 11: [mp4] [mkv]
• Lecture 12: [mp4] [mkv]

Homework Sets

There will be biweekly mandatory homework, which will typically be released on wednesdays.

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5

Literature

The first part of the lecture will be on basic results for which the following books can be useful.

• Vazirani, Vijay V.: Approximation Algorithms, Springer-Verlag, 2001.
• Approximation Algorithms for NP-hard problems edited by Dorit S. Hochbaum, more info.
• The Design of Approximation Algorithms by David P. Williamson and David B. Shmoys, published by Cambridge University Press. more info

The second part of the lecture will be on recent results for which the corresponding papers will be announced in due time.

Mailing List

There will be a mailing list. We will distribute the homework sets and other announcements via this list, so, please subscribe!

You may also want to check out the alg-studs mailing list which is similiar to cs-studs but for algorithmic students.