Approximation Algorithms

Lecture: Tuesdays, 3PM, weekly in room SN 19.3
Tutorials: Wednesdays, 11:30AM, in room SN 19.4

First lecture: The first lecture will be held on 25.04.2023
First Tutorial: The first tutorial will be held on 03.05.2023

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 may be missing or outdated.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

Video recordings of the previous version of this course are also available and will be provided after each lecture. Please do not hesitate to contact us if there are any problems with the videos. If you do encounter a problem while playing the recordings in your browser, consider downloading the video and playing it in a regular video player. The videos are 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]

Slides

Here are the review slides from the last lecture:

• Review.pdf

Homework Sets

The homework assignment sheets will be published below.

• Homework 1 (Solutions discussed in the tutorial session, dated May 24th)
  Update (May, 12th): Typo fixed in exercise 4.
• Homework 2 (Solutions discussed in the tutorial session, dated June 7th)
• Homework 3 (Solutions discussed in the tutorial session, dated June 21th)
• Homework 4 (Solutions discussed in the tutorial session, dated July 5th)
• Homework 5 (Solutions will be discussed in the tutorial session, dated July 19th)

Literature

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

• Vazirani, Vijay V.: Approximation Algorithms, Springer-Verlag, 2001 [PDF].
• 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 (online). 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 is 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 similar to cs-studs but for algorithmic students.