# NDAK14005U Randomised Algorithms (RA)

Volume 2021/2022
Education

MSc Programme in Bioinformatics

MSc Programme in Computer Science

Content

Randomised algorithms are often far superior to their traditional deterministic counterparts, both in efficiency and simplicity. Many computational tasks are fundamentally impossible without randomisation. However, mastering randomised algorithms requires a basic mathematical understanding of the relevant combinatorial probability theory, and therefore a regular algorithms course will normally either skip them or teach them very superficially. Randomisation is a way of thinking, that needs a proper introduction. Applications in many areas will be considered, e.g., graph algorithms, machine learning, distributed computing, and geometry, but the focus will be on the general understanding, the goal being to give the students the foundation needed to understand and use randomisation, no matter what application area they may later be interested in.

Learning Outcome

Knowledge of

The relevant combinatorial probability theory and randomised techniques in algorithms:

• Game-Theoretic Techniques
• Moments and Deviations
• Tail Inequalities
• The Probabilistic Method
• Randomised Data Structures
• Randomised Geometric Algorithms
• Randomised Graph Algorithms
• Randomised Distributed and Parallel Algorithms

Skills in

• Proving bounds on the expected running time of randomised algorithms
• Explaining methods for bounding the probability that a random variable deviates far from its expectation
• Applying the probabilistic method to prove the existence of e.g. algorithms
• Giving simple and efficient algorithms and data structures using randomisation where more traditional deterministic approaches are more cumbersome or less efficient

Competences to

• Reason about and apply randomised techniques to computational problems that the student may later encounter in life.

See Absalon for a list of course literature.

The students should enjoy mathematics, 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.
This course has considerable overlap with the BSc-level course "Randomiserede algoritmer for dataanalyse". It is not recommended that you take this course if you have already taken the other. For details, contact the course organiser.
• Category
• Hours
• Lectures
• 36
• Preparation
• 85
• Theory exercises
• 84
• Exam
• 1
• Total
• 206
Written
Individual
Continuous feedback during the course of the semester
Credit
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. 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

Same as ordinary exam.

If the student is not yet qualified, then qualification can be achieved by submitting the missing assignments. The missing assignments must be submitted no later than two weeks before the re-exam date in order to qualify for the re-exam.

##### Criteria for exam assesment

See Learning Outcome.