The course covers the fundamentals of complexity theory and algorithm design with applications in networked system optimization and sequential decision making. The course is intended for PhD students who perform research in the ICT area, and it prepares the students to use rigorous methods for proving the complexity of optimization problems and for designing approximation algorithms with provable worst case performance bounds for computationally intractable problems.
Course offering missing
Course offering missing for current semester as well as for previous and coming semestersInformation for research students about course offerings
The course is given in every second year, in P2.
Content and learning outcomes
Course contents
1. Problems, algorithms and complexity, polynomial time, NP-complete and NP-hard problems
2. Examples of polynomial time problems on graphs, greedy algorithms, networking examples
3. Famous NP-complete problems, proof of NP completeness, problems beyond NP,
4. Polynomial-time reduction, NP-hard problems, networking examples
5. Approximation methods and algorithms – greedy strategy, restriction, partition
6. Approximation methods and algorithms – relaxation, primal-dual schemes and local ratio
7. Proof of complexity and algorithm design for networking problems based on recent literature
Intended learning outcomes
After the course the students should be able to:
- Correctly define computational complexity classes and analyze the complexity of algorithms;
- Discuss basic problems in areas of graph theory, sets and partitions, storage and scheduling;
- Formulate network design problems as decision or discrete optimization problems;
- Present procedures of proving NP-completeness and NP-hardness, and be able to provide proofs for basic examples;
- Use approximation algorithms to cope with NP-hard problems.
Course Disposition
8 lectures, 2 seminars with student presentations, 3 home assignments, final exam.
Literature and preparations
Specific prerequisites
PhD student
Recommended prerequisites
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Equipment
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Literature
- J. Kleinberg, É. Tardos, “Algorithm Design” Pearson Education, 2014
- Ding-Zhu. Du Ker-I Ko; Xiaodong Hu, “Design and Analysis of Approximation Algorithms”, Springer Optimization and Its Applications vol 62
- Extracts of M.R. Garey and D.S.Johnson, “Computers and Intractability,” W. H. Freeman, 1979
- Relevant journal papers with networking applications, provided before course start.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
- Active participation on the lectures
- 30 min oral presentation on one of the seminars
- 80% on homework problems
- 80% on the final exam
Opportunity to complete the requirements via supplementary examination
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Opportunity to raise an approved grade via renewed examination
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Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course web
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Offered by
Main field of study
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Education cycle
Third cycle
Add-on studies
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