DD2350 Algorithms, Data Structures and Complexity 9.5 credits

Design principles of algorithms: Decomposition, greedy algorithms, dynamic programming, local and exhaustive search. Algorithm analysis. Approximation algorithms and heuristics. Applications with algorithms for problems on sets, graphs, arithmetic and geometry. Implementation of algorithms.

Data structures: Review of hash tables and heaps; balanced trees, Bloom filters, persistent data structures Use and implementation of data structures. Computability and complexity: The concept of reduction, the complexity classes P (polynomial time) and NP (non-deterministic polynomial time). NP-complete problems, undecidable problems. Coping with computationally intractable problems.

Terminology in Swedish and English.

After passing the course, the student should be able to

• develop and implement algorithms with data structures and analyse them with respect to correctness and efficiency
• compare alternative algorithms and data structures regarding efficiency and reliability
• define and translate central concepts such as P, NP, NP-completeness and undecidability
• compare problems with respect to complexity by means of reductions
• handle problems with high complexity

in order to

• independently be able to design computer programs that use time and memory efficiently and thereby can contribute to economically and environmentally sustainable development
• in professional life identify and attack problems that are unrealistically resource demanding or not possible to solve on a computer.

Knowledge and skills in programming, 6 credits, equivalent to completed course DD1337/DD1310-DD1318/DD1321/DD1331/DD100N/ID1018.

Knowledge in foundations of computer science, 6 credits, equivalent to completed course DD1338/DD1320-DD1327/DD2325/ID1020/ID1021.

Knowledge in discrete mathematics, 3 higher education credits, equivalent to completed course SF1671/SF1610/SF1630/SF1662/SF1679.

Knowledge in algebra and geometry, 7.5 higher education credits, equivalent to completed course SF1624.

Knowledge in calculus in one variable, 7.5 higher education credits, equivalent to completed course SF1625.

Active participation in a course offering where the final examination is not yet reported in LADOK is considered equivalent to completion of the course.
Being registered for a course counts as active participation.
The term 'final examination' encompasses both the regular examination and the first re-examination.

Good programming skills (equivalent to DD1337/DD1310-1319/DD1331/DD1332/ID1018). For lab 2, some knowledge of Java programming is needed. In some of the labs in the course, a more efficient programming language than Python has to be used, e.g. Java or C/C++.

Concepts from algorithms and data structures (equivalent to DD1338/DD1320-DD1328/ID1021) including algorithm analysis, time complexity, pseudocode, algorithm justification, algorithms for searching and sorting, data structures: lists, queues, stacks, sets, binary trees, priority queues, hash tables.

Concepts from probability theory (equivalent to SF1900-SF1935) including probability, conditional probability, independence, expectation.

Concepts from logic (equivalent to DD1351) including propositional logic, induction, and program verification.

Concepts from algebra and geometry (equivalent to SF1624) including vectors, matrices, systems of linear equations, vector geometry with scalar and vector products.

Concepts from single-variable calculus (equivalent to SF1625) including functions, domains, ranges, increasing and decreasing functions, exponential functions and logarithms, power laws, logarithmic laws, limits, l'Hôpital's rule, sequences, and series.

Concepts from discrete mathematics including sets, induction, recurrence equations, numeral systems, divisibility, Euclid's algorithm, prime numbers, unique factorization, modular arithmetic, graphs, Eulerian circuits, Hamiltonian cycles, trees, graph coloring, bipartite graphs, permutations, rings. Anyone who has not completed 7.5 credits of discrete mathematics equivalent to SF1610/SF1630/SF1662/SF1679 by the start of the course must take SF1688 in parallel with DD2350, see additional regulations in the course syllabus.

• Algorithm Design by Kleinberg-Tardos, Pearson, 2014, ISBN 978-1292023946.

• Algorithms and Complexity, a supplement to Algorithm Design, Pearson Custom Publishing, ISBN 978-1847764126.

If the course is discontinued, students may request to be examined during the following two academic years.

• LAB1 - Laboratory assignments, 4.0 credits, grading scale: A, B, C, D, E, FX, F
• MAS1 - Individual master´s test, 1.5 credits, grading scale: A, B, C, D, E, FX, F
• MAS2 - Individual master´s test, 1.5 credits, grading scale: A, B, C, D, E, FX, F
• TEN1 - Theory examination, 2.5 credits, grading scale: P, F

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.

The grade for LAB1 depends on how many computer labs are presented orally within the specified time.

The master's tests are constituted by individual assignments that are reported both in writing and orally

Optional theoretical assignments with peer assessment that will give bonus points to the theory examination.
The theory exam is conducted as a digital quiz with subsequent peer assessment.

The requirements for E/pass for the components MAS1, MAS2 and TEN1 can be completed via supplementary examination for students receiving grade Fx. A passed individual lab assignment can be credited in later course offerings if the assignment is unchanged.

An approved grade can be raised for MAS1 and MAS2 in a later course offering. For LAB1, only grades B and C can be raised, with the grade rising lab in a later course offering. It is not possible to receive new lab delivery points in a later course offering.

Viggo Kann

• 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.

DD2440 Advanced Algorithms, DD2542 Seminars in Theoretical Computer Science, Algorithms and Complexity, DD2445 Complexity Theory, DD2448 Foundations of Cryptography, and DD2458 Problem Solving and Programming under Pressure.

Information before you start the course.

Information on assessment of assignments after the end of the course.

Grading critera will be published at the start of the course.

DD2350 cannot be combined with DD1352, DD2352, or DD2354.

In this course, the EECS code of honor applies, see:
http://www.kth.se/en/eecs/utbildning/hederskodex

A student who, at the beginning of the course, has not completed 7.5 higher education credits of discrete mathematics, equivalent to SF1610/SF1630/SF1662/SF1679, must take SF1688 in parallel with DD2350.