Search result: Catalogue data in Spring Semester 2023
Computer Science Master  | ||||||||||||||||||||||||||||||||||||
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| Minor in Theoretical Computer Science | ||||||||||||||||||||||||||||||||||||
| Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||
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| 272-0300-00L | Algorithmics for Hard Problems This course d o e s n o t include the Mentored Work Specialised Courses with an Educational Focus in Computer Science A. | W | 5 credits | 2V + 1U + 1A | H.‑J. Böckenhauer, D. Komm | |||||||||||||||||||||||||||||||
| Abstract | This course unit looks into algorithmic approaches to the solving of hard problems, particularly with moderately exponential-time algorithms and parameterized algorithms. The seminar is accompanied by a comprehensive reflection upon the significance of the approaches presented for computer science tuition at high schools. | |||||||||||||||||||||||||||||||||||
| Learning objective | To systematically acquire an overview of the methods for solving hard problems. To get deeper knowledge of exact and parameterized algorithms. | |||||||||||||||||||||||||||||||||||
| Content | First, the concept of hardness of computation is introduced (repeated for the computer science students). Then some methods for solving hard problems are treated in a systematic way. For each algorithm design method, it is discussed what guarantees it can give and how we pay for the improved efficiency. A special focus lies on moderately exponential-time algorithms and parameterized algorithms. | |||||||||||||||||||||||||||||||||||
| Lecture notes | Unterlagen und Folien werden zur Verfügung gestellt. | |||||||||||||||||||||||||||||||||||
| Literature | J. Hromkovic: Algorithmics for Hard Problems, Springer 2004. R. Niedermeier: Invitation to Fixed-Parameter Algorithms, 2006. M. Cygan et al.: Parameterized Algorithms, 2015. F. Fomin et al.: Kernelization, 2019. F. Fomin, D. Kratsch: Exact Exponential Algorithms, 2010. | |||||||||||||||||||||||||||||||||||
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| 272-0302-00L | Approximation and Online Algorithms Does not take place this semester. | W | 5 credits | 2V + 1U + 1A | 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. | |||||||||||||||||||||||||||||||||||
| Learning 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 | |||||||||||||||||||||||||||||||||||
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| 401-3052-10L | Graph Theory | W | 10 credits | 4V + 1U | B. Sudakov | |||||||||||||||||||||||||||||||
| Abstract | Basics, trees, Caley's formula, matrix tree theorem, connectivity, theorems of Mader and Menger, Eulerian graphs, Hamilton cycles, theorems of Dirac, Ore, Erdös-Chvatal, matchings, theorems of Hall, König, Tutte, planar graphs, Euler's formula, Kuratowski's theorem, graph colorings, Brooks' theorem, 5-colorings of planar graphs, list colorings, Vizing's theorem, Ramsey theory, Turán's theorem | |||||||||||||||||||||||||||||||||||
| Learning 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. | |||||||||||||||||||||||||||||||||||
| 401-3902-21L | Network & Integer Optimization: From Theory to Application | W | 6 credits | 3G | R. Zenklusen | |||||||||||||||||||||||||||||||
| Abstract | This course covers various topics in Network and (Mixed-)Integer Optimization. It starts with a rigorous study of algorithmic techniques for some network optimization problems (with a focus on matching problems) and moves to key aspects of how to attack various optimization settings through well-designed (Mixed-)Integer Programming formulations. | |||||||||||||||||||||||||||||||||||
| Learning objective | Our goal is for students to both get a good foundational understanding of some key network algorithms and also to learn how to effectively employ (Mixed-)Integer Programming formulations, techniques, and solvers, to tackle a wide range of discrete optimization problems. | |||||||||||||||||||||||||||||||||||
| Content | Key topics include: - Matching problems; - Integer Programming techniques and models; - Extended formulations and strong problem formulations; - Solver techniques for (Mixed-)Integer Programs; - Decomposition approaches. | |||||||||||||||||||||||||||||||||||
| Literature | - Bernhard Korte, Jens Vygen: Combinatorial Optimization. 6th edition, Springer, 2018. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. This work has 3 volumes. - Vanderbeck François, Wolsey Laurence: Reformulations and Decomposition of Integer Programs. Chapter 13 in: 50 Years of Integer Programming 1958-2008. Springer, 2010. - Alexander Schrijver: Theory of Linear and Integer Programming. John Wiley, 1986. | |||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Solid background in linear algebra. Preliminary knowledge of Linear Programming is ideal but not a strict requirement. Prior attendance of the course Linear & Combinatorial Optimization is a plus. | |||||||||||||||||||||||||||||||||||
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| 402-0448-01L | Quantum Information Processing I: Concepts This theory part QIP I together with the experimental part 402-0448-02L QIP II (both offered in the Spring Semester) combine to the core course in experimental physics "Quantum Information Processing" (totally 10 ECTS credits). This applies to the Master's degree programme in Physics. | W | 5 credits | 2V + 1U | J. Home | |||||||||||||||||||||||||||||||
| Abstract | The course covers the key concepts of quantum information processing, including quantum algorithms which give the quantum computer the power to compute problems outside the reach of any classical supercomputer. Key concepts such as quantum error correction are discussed in detail. They provide fundamental insights into the nature of quantum states and measurements. | |||||||||||||||||||||||||||||||||||
| Learning objective | By the end of the course students are able to explain the basic mathematical formalism of quantum mechanics and apply them to quantum information processing problems. They are able to adapt and apply these concepts and methods to analyse and discuss quantum algorithms and other quantum information-processing protocols. | |||||||||||||||||||||||||||||||||||
| Content | The topics covered in the course will include quantum circuits, gate decomposition and universal sets of gates, efficiency of quantum circuits, quantum algorithms (Shor, Grover, Deutsch-Josza,..), quantum error correction, fault-tolerant designs, and quantum simulation. | |||||||||||||||||||||||||||||||||||
| Lecture notes | Will be provided. | |||||||||||||||||||||||||||||||||||
| Literature | Quantum Computation and Quantum Information Michael Nielsen and Isaac Chuang Cambridge University Press | |||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | A good understanding of finite dimensional linear algebra is recommended. | |||||||||||||||||||||||||||||||||||
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