# NDAK16001U  Approximation Algorithms (APX)

Volume 2018/2019
Education

MSc Programme in Computer Science

Content

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.

Learning Outcome

Knowledge of

• 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

Skills in

• 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

Competences to

• 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)

The students should be comfortable with formal, mathematical reasoning, as the course uses the power of mathematics to understand and prove good performance of algorithms. It is assumed that the students have completed an algorithms course such as Advanced Algorithms and Data Structures, and are comfortable using mathematical proofs in the analysis of algorithms.
Lectures and compulsory assignments.
Written
Individual
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 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.

Aid
All aids allowed
Marking scale
Censorship form
No external censorship
Several internal examiners
Re-exam

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.

• Category
• Hours
• Lectures
• 36
• Theory exercises
• 84
• Preparation
• 85
• Exam
• 1
• Total
• 206