NDAK16001U Approximation Algorithms (APX)
MSc Programme in Computer Science
Many optimization problems in the real world are NP-hard meaning that we cannot hope to solve them optimally. Instead, we use approximation algorithms to find solutions that are provably close in quality to the optimal solutions.
The course is of a theoretical nature, giving the students general guidelines for developing and analyzing approximation algorithms for various optimization problems. It is aimed at graduate students who like to use mathematics to solve algorithmic problems.
The topics mentioned under Learning Outcome are covered in lectures and worked on in exercises in order to develop the necessary skills and competences.
- Greedy algorithms and local search
- Rounding data and dynamic programming
- Deterministic rounding of linear programs
- Random sampling and randomized rounding of linear programs
- Randomized rounding of semidefinite programs
- The primal-dual method
- Cuts and metrics
- Further uses of the different techniques in various application areas
- Proving approximation guarantees for different types of algorithms
- Using linear programming, both with rounding and as a theoretical basis for primal-dual algorithms
- Analyzing greedy algorithms and local search algorithms
- Apply approximation algorithms to computational problems that the student may later encounter in life.
- Communicate effectively about the theory of approximation algorithms, both for accessing advanced topics from the research literature, and for convincingly presenting the results of own work.
Expected to be "The Design of Approximation Algorithms" by Shmoys and Williamson (is available for free online)
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutes30 minutes preparation, 30 minutes oral examination, including grade determination.
- Exam registration requirements
The student must solve mandatory assignments during the course. Assignments will be made each week and be due in the following week. 5 out of 7 assignments must be submitted and approved by the due date in order to qualify for the exam.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
Re-exam same as ordinary exam.
If the student is not yet qualified, then qualification can be achieved by handing-in the missing assignments. The missing assignments must be submitted and approved no later than two weeks before the re-exam date in order to qualify for the exam.
Criteria for exam assesment
See Learning Outcome.
- Theory exercises