# Search result: Catalogue data in Spring Semester 2020

Computer Science Master | ||||||

Focus Courses | ||||||

Focus Courses in Theoretical Computer Science | ||||||

Focus Elective Courses Theoretical Computer Science | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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252-0408-00L | Cryptographic Protocols | W | 6 credits | 2V + 2U + 1A | M. Hirt, U. Maurer | |

Abstract | The course presents a selection of hot research topics in cryptography. The choice of topics varies and may include provable security, interactive proofs, zero-knowledge protocols, secret sharing, secure multi-party computation, e-voting, etc. | |||||

Objective | Indroduction to a very active research area with many gems and paradoxical results. Spark interest in fundamental problems. | |||||

Content | The course presents a selection of hot research topics in cryptography. The choice of topics varies and may include provable security, interactive proofs, zero-knowledge protocols, secret sharing, secure multi-party computation, e-voting, etc. | |||||

Lecture notes | the lecture notes are in German, but they are not required as the entire course material is documented also in other course material (in english). | |||||

Prerequisites / Notice | A basic understanding of fundamental cryptographic concepts (as taught for example in the course Information Security or in the course Cryptography Foundations) is useful, but not required. | |||||

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. | |||||

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. | |||||

263-4507-00L | Advances in Distributed Graph AlgorithmsDoes not take place this semester. | W | 6 credits | 3V + 1U + 1A | M. Ghaffari | |

Abstract | How can a network of computers solve the graph problems needed for running that network? | |||||

Objective | This course will familiarize the students with the algorithmic tools and techniques in local distributed graph algorithms, and overview the recent highlights in the field. This will also prepare the students for independent research at the frontier of this area. This is a special‐topics course in algorithm design. It should be accessible to any student with sufficient theoretical/algorithmic background. In particular, it assumes no familiarity with distributed computing. We only expect that the students are comfortable with the basics of algorithm design and analysis, as well as probability theory. It is possible to take this course simultaneously with the course “Principles of Distributed Computing”. If you are not sure whether you are ready for this class or not, please consult the instructor. | |||||

Content | How can a network of computers solve the graph problems needed for running that network? Answering this and similar questions is the underlying motivation of the area of Distributed Graph Algorithms. The area focuses on the foundational algorithmic aspects in these questions and provides methods for various distributed systems --- e.g., the Internet, a wireless network, a multi-processor computer, etc --- to solve computational problems that can be abstracted as graph problems. For instance, think about shortest path computation in routing, or about coloring and independent set computation in contention resolution. Over the past decade, we have witnessed a renaissance in the area of Distributed Graph Algorithms, with tremendous progress in many directions and solutions for a number of decades-old central problems. This course overviews the highlights of these results. The course will mainly focus on one half of the field, which revolves around locality and local problems. The other half, which relates to the issue of congestion and dealing with limited bandwidth in global problems, will not be addressed in this offering of the course. The course will cover a sampling of the recent developments (and open questions) at the frontier of research of distributed graph algorithms. The material will be based on a compilation of recent papers in this area, which will be provided throughout the semester. The tentative list of topics includes: - The shattering technique for local graph problems and its necessity - Lovasz Local Lemma algorithms, their distributed variants, and distributed applications - Distributed Derandomization - Distributed Lower bounds - Graph Coloring - Complexity Hierarchy and Gaps - Primal-Dual Techniques | |||||

Prerequisites / Notice | The class assumes no knowledge in distributed algorithms/computing. Our only prerequisite is the undergraduate class Algorithms, Probability, and Computing (APC) or any other course that can be seen as the equivalent. In particular, much of what we will discuss uses randomized algorithms and therefore, we will assume that the students are familiar with the tools and techniques in randomized algorithms and analysis (to the extent covered in the APC class). | |||||

263-4656-00L | Digital Signatures | W | 4 credits | 2V + 1A | D. Hofheinz | |

Abstract | Digital signatures as one central cryptographic building block. Different security goals and security definitions for digital signatures, followed by a variety of popular and fundamental signature schemes with their security analyses. | |||||

Objective | The student knows a variety of techniques to construct and analyze the security of digital signature schemes. This includes modularity as a central tool of constructing secure schemes, and reductions as a central tool to proving the security of schemes. | |||||

Content | We will start with several definitions of security for signature schemes, and investigate the relations among them. We will proceed to generic (but inefficient) constructions of secure signatures, and then move on to a number of efficient schemes based on concrete computational hardness assumptions. On the way, we will get to know paradigms such as hash-then-sign, one-time signatures, and chameleon hashing as central tools to construct secure signatures. | |||||

Literature | Jonathan Katz, "Digital Signatures." | |||||

Prerequisites / Notice | Ideally, students will have taken the D-INFK Bachelors course "Information Security" or an equivalent course at Bachelors level. | |||||

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 | |||||

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) | |||||

272-0300-00L | Algorithmics for Hard Problems Does not take place this semester. 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 | ||

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. | |||||

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, D. Kratsch: Exact Exponential Algorithms, 2010. |

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