Search result: Catalogue data in Spring Semester 2020

Cyber Security Master Information
Minor
Theoretical Computer Science
Elective Courses
NumberTitleTypeECTSHoursLecturers
252-1424-00LModels of ComputationW6 credits2V + 2U + 1AM. Cook
AbstractThis course surveys many different models of computation: Turing Machines, Cellular Automata, Finite State Machines, Graph Automata, Circuits, Tilings, Lambda Calculus, Fractran, Chemical Reaction Networks, Hopfield Networks, String Rewriting Systems, Tag Systems, Diophantine Equations, Register Machines, Primitive Recursive Functions, and more.
ObjectiveThe goal of this course is to become acquainted with a wide variety of models of computation, to understand how models help us to understand the modeled systems, and to be able to develop and analyze models appropriate for new systems.
ContentThis course surveys many different models of computation: Turing Machines, Cellular Automata, Finite State Machines, Graph Automata, Circuits, Tilings, Lambda Calculus, Fractran, Chemical Reaction Networks, Hopfield Networks, String Rewriting Systems, Tag Systems, Diophantine Equations, Register Machines, Primitive Recursive Functions, and more.
272-0302-00LApproximation and Online Algorithms Information W5 credits2V + 1U + 1AH.‑J. Böckenhauer, D. Komm
AbstractThis lecture deals with approximative algorithms for hard optimization problems and algorithmic approaches for solving online problems as well as the limits of these approaches.
ObjectiveGet a systematic overview of different methods for designing approximative algorithms for hard optimization problems and online problems. Get to know methods for showing the limitations of these approaches.
ContentApproximation algorithms are one of the most succesful techniques to attack hard optimization problems. Here, we study the so-called approximation ratio, i.e., the ratio of the cost of the computed approximating solution and an optimal one (which is not computable efficiently).
For an online problem, the whole instance is not known in advance, but it arrives pieceweise and for every such piece a corresponding part of the definite output must be given. The quality of an algorithm for such an online problem is measured by the competitive ratio, i.e., the ratio of the cost of the computed solution and the cost of an optimal solution that could be given if the whole input was known in advance.

The contents of this lecture are
- the classification of optimization problems by the reachable approximation ratio,
- systematic methods to design approximation algorithms (e.g., greedy strategies, dynamic programming, linear programming relaxation),
- methods to show non-approximability,
- classic online problem like paging or scheduling problems and corresponding algorithms,
- randomized online algorithms,
- the design and analysis principles for online algorithms, and
- limits of the competitive ratio and the advice complexity as a way to do a deeper analysis of the complexity of online problems.
LiteratureThe lecture is based on the following books:

J. Hromkovic: Algorithmics for Hard Problems, Springer, 2004

D. Komm: An Introduction to Online Computation: Determinism, Randomization, Advice, Springer, 2016

Additional literature:

A. Borodin, R. El-Yaniv: Online Computation and Competitive Analysis, Cambridge University Press, 1998
263-4400-00LAdvanced Graph Algorithms and Optimization Information Restricted registration - show details
Number of participants limited to 30.
W5 credits3G + 1AR. Kyng
AbstractThis course will cover a number of advanced topics in optimization and graph algorithms.
ObjectiveThe course will take students on a deep dive into modern approaches to
graph algorithms using convex optimization techniques.

By studying convex optimization through the lens of graph algorithms,
students should develop a deeper understanding of fundamental
phenomena in optimization.

The course will cover some traditional discrete approaches to various graph
problems, especially flow problems, and then contrast these approaches
with modern, asymptotically faster methods based on combining convex
optimization with spectral and combinatorial graph theory.
ContentStudents should leave the course understanding key
concepts in optimization such as first and second-order optimization,
convex duality, multiplicative weights and dual-based methods,
acceleration, preconditioning, and non-Euclidean optimization.

Students will also be familiarized with central techniques in the
development of graph algorithms in the past 15 years, including graph
decomposition techniques, sparsification, oblivious routing, and
spectral and combinatorial preconditioning.
Prerequisites / NoticeThis course is targeted toward masters and doctoral students with an
interest in theoretical computer science.

Students should be comfortable with design and analysis of algorithms, probability, and linear algebra.

Having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, but not formally required. If you are not
sure whether you're ready for this class or not, please consult the
instructor.
401-3052-05LGraph Theory Information W5 credits2V + 1UB. Sudakov
AbstractBasic notions, trees, spanning trees, Caley's formula, vertex and edge connectivity, 2-connectivity, Mader's theorem, Menger's theorem, Eulerian graphs, Hamilton cycles, Dirac's theorem, matchings, theorems of Hall, König and Tutte, planar graphs, Euler's formula, basic non-planar graphs, graph colorings, greedy colorings, Brooks' theorem, 5-colorings of planar graphs
ObjectiveThe students will get an overview over the most fundamental questions concerning graph theory. We expect them to understand the proof techniques and to use them autonomously on related problems.
Lecture notesLecture will be only at the blackboard.
LiteratureWest, D.: "Introduction to Graph Theory"
Diestel, R.: "Graph Theory"

Further literature links will be provided in the lecture.
Prerequisites / NoticeStudents are expected to have a mathematical background and should be able to write rigorous proofs.


NOTICE: This course unit was previously offered as 252-1408-00L Graphs and Algorithms.
401-3903-11LGeometric Integer ProgrammingW6 credits2V + 1UJ. Paat
AbstractInteger programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
ObjectiveThe purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
ContentKey topics are:

- Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension.

- Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems

- Duality theory for integer optimization problems from the vantage point of lattice free sets.
Lecture notesnot available, blackboard presentation
LiteratureLecture notes will be provided.

Other helpful materials include

Bertsimas, Weismantel: Optimization over Integers, 2005

and

Schrijver: Theory of linear and integer programming, 1986.
Prerequisites / Notice"Mathematical Optimization" (401-3901-00L)
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