Search result: Catalogue data in Spring Semester 2020
Cyber Security Master | ||||||
Minor | ||||||
Theoretical Computer Science | ||||||
Elective Courses | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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252-1424-00L | Models of Computation | W | 6 credits | 2V + 2U + 1A | M. Cook | |
Abstract | This 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. | |||||
Objective | The 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. | |||||
Content | This 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. | |||||
272-0302-00L | Approximation and Online Algorithms | W | 5 credits | 2V + 1U + 1A | H.‑J. Böckenhauer, D. Komm | |
Abstract | This lecture deals with approximative algorithms for hard optimization problems and algorithmic approaches for solving online problems as well as the limits of these approaches. | |||||
Objective | Get 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. | |||||
Content | Approximation 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. | |||||
Literature | The 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 | |||||
263-4400-00L | Advanced Graph Algorithms and Optimization Number of participants limited to 30. | W | 5 credits | 3G + 1A | R. Kyng | |
Abstract | This course will cover a number of advanced topics in optimization and graph algorithms. | |||||
Objective | The 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. | |||||
Content | Students 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 / Notice | This 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. | |||||
401-3052-05L | Graph Theory | W | 5 credits | 2V + 1U | B. Sudakov | |
Abstract | Basic 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 | |||||
Objective | The 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 notes | Lecture will be only at the blackboard. | |||||
Literature | West, D.: "Introduction to Graph Theory" Diestel, R.: "Graph Theory" Further literature links will be provided in the lecture. | |||||
Prerequisites / Notice | Students 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. | |||||
401-3903-11L | Geometric Integer Programming | W | 6 credits | 2V + 1U | J. Paat | |
Abstract | Integer 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. | |||||
Objective | The purpose of the lecture is to provide a geometric treatment of the theory of integer optimization. | |||||
Content | Key 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 notes | not available, blackboard presentation | |||||
Literature | Lecture 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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