# 2022/2023

## Content, progress and pedagogy of the module

Disclaimer.
This is an English translation of the module. In case of discrepancy between the translation and the Danish version, the Danish version of the module is valid.

### Learning objectives

#### Knowledge

The student must gain knowledge of the following theories and methods:

• algorithm design techniques such as share-and-rule, greedy algorithms, dynamic programming, backtracking, branch-and-bound algorithms, randomized algorithms and linear programming
• techniques in advanced algorithm analysis such as amortized analysis, analysis of expected complexity and experiments with algorithms
• examples of core algorithms and data structures for solving a number of problems from different areas of computer science such as algorithms for external memory, multi-threaded algorithms, search in text, advanced graph algorithms and geometric calculations
• computability theory: Turing machines; Church-Turing thesis; decidable and recognizable languages; examples of undecidable problems, including the proofs via reduction
• complexity theory: deterministic and nondeterministic Turing machines and their time complexity; time complexity classes; polynomial reductions; NP completeness; examples of NP-complete problems

#### Skills

• explain the principles behind the most important algorithm design and analysis techniques

• select and apply algorithm design and analysis techniques for a given problem

• recognize a range of problems from different areas of computer science and select the most appropriate algorithms and data structures to solve them

• be able to account accurately and using the subject's terminology and notation for important results within calculation complexity and for how and to what extent these results can be used to classify calculation problems, including complexity analysis and applications of reductions

• be able to categorize computational problems  as dedidable/undecidable and argue that concrete problems are NP-hard by using the notion of reduction

SKILL OBJECTIVE APPLICABLE TO STUDENTS STUDYING AT CANDIDATE LEVEL, BUT FOLLOWING TEACHING AT BACHELOR LEVEL:

• understand and apply the principles of proof techniques covered in the course with a focus on mathematical precision of the arguments.

#### Competences

• be able to apply concepts and techniques within computational complexity to analysis of computational problems
• when facing a computer science problem, be able to develop and analyze efficient algorithms and data structures for solving the problem

### Type of instruction

The teaching is organized in accordance with the general teaching methods for the education, cf. section 17.

The student is expected to spend 30 hours per ECTS, which for this activity means 150 hours.

## Exam

### Exams

 Name of exam Algorithms and Computability Type of exam Written or oral exam ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment The criteria of assessment are stated in the Examination Policies and Procedures