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Kurs: 03-IMAT-APX Approximation Algorithms - Details

Kurs: 03-IMAT-APX Approximation Algorithms - Details

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General information

Course name Kurs: 03-IMAT-APX Approximation Algorithms
Subtitle
Course number 03-IMAT-APX
Semester SoSe 2025
Current number of participants 34
Home institute Informatik
Courses type Kurs in category Teaching
First date Thursday, 10.04.2025 14:00 - 16:00, Room: MZH 1450
Type/Form
Performance record Oral exam
Englischsprachige Veranstaltung Ja
Miscellanea This course deals with the design and analysis of algorithms for combinatorial optimization problems such as they arise in communication, project planning, and logistics. These problems are typically computationally intractable and one often resorts to heuristics that provide sufficiently good solutions in reasonable amount of runtime.
However, in most cases, such heuristics do not provide any hard guarantees on the performance in comparison to the optimum solution. In this course, we study polynomial-time algorithms for combinatorial optimization problems which can provide strong mathematical guarantees on the worst-case performance. Topics include:
- Greedy algorithms and Local Search
- Rounding Data and Dynamic Programming
- Deterministic Rounding of Linear Programs (LPs)
- Random Sampling and Randomized Rounding of LPs
- Primal-Dual Methods
- Hardness of Approximation
- Problem Solving under Uncertainty

Format and Examination
We will teach the course with 4 hours per week (6 ECTS), where roughly every other week one class will be an interactive exercise session.

There is the possibility to further extend the content of the course as well as the credits by participating in a seminar. This participation consists of individually studying a recent research article and presenting the main results to the rest of the class.
ECTS points 6

Rooms and times

MZH 1470
Tuesday: 10:00 - 12:00, weekly (12x)
MZH 1450
Thursday: 14:00 - 16:00, weekly (12x)

Module assignments

Comment/Description

Profil: SQ, KIKR.
Schwerpunkt: IMA-SQ, IMVT-AI, IMVT-VMC
weitere Studiengänge: M-M-Alg-Num, M-T
https://lvb.informatik.uni-bremen.de/imat/03-imat-apx.pdf

A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be modeled as combinatorial optimization problems. In most cases, these problems are computationally intractable and one often resorts to heuristics that provide sufficiently good solutions in reasonable amount of runtime. However, in most cases, such heuristics do not provide a worst case guarantee on the performance in comparison to the optimum solution. In this course, we shall study algorithms for combinatorial optimization problems which can provide strong mathematical guarantees on performance. The course aims at developing a toolkit for solving such problems. The lectures will consist of designing polynomial-time algorithms and proving rigorous bounds on their worst case performances.
We review many classical results in the field of approximation algorithms, highlighting different techniques commonly used for the design of such algorithms. Among others, we will treat the following topics:
• Greedy algorithms and Local Search
• Rounding Data and Dynamic Programming
• Deterministic Rounding of Linear Programs (LPs)
• Random Sampling and Randomized Rounding of LPs
• Primal-Dual Methods
• Hardness of Approximation
• Problem Solving under Uncertainty