NDAK16001U Approximation Algorithms (APX)

Volume 2020/2021

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 analysing 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

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
  • Analysing 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.

See Absalon when the course is set up.

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.

Academic qualifications equivalent to a BSc degree is recommended.
Lectures and compulsory assignments.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 85
  • Theory exercises
  • 84
  • Exam
  • 1
  • Total
  • 206
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (including grading)
The oral examination is with 30 minutes preparation
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. 4 out of 6 assignments must be submitted timely and approved 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 the ordinary exam.

If the student is not yet qualified to participating in the exam, then qualification can be achieved by handing-in the missing/not-approved assignments. The missing/not-approved assignments must be submitted and approved no later than three weeks before the re-exam week in order to qualify for the re-exam.



Criteria for exam assesment

See Learning Outcome.