Search result: Catalogue data in Spring Semester 2018
|Computer Science Master|
|Focus Courses in Theoretical Computer Science|
|Focus Elective Courses Theoretical Computer Science|
|252-0408-00L||Cryptographic Protocols||W||5 credits||2V + 2U||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.
|252-1403-00L||Invitation to Quantum Informatics||W||3 credits||2V||S. Wolf|
|Abstract||Followed by an introduction to the basic principles of quantum physics, such as superposition, interference, or entanglement, a variety of subjects are treated: Quantum algorithms, teleportation, quantum communication complexity and "pseudo-telepathy", quantum cryptography, as well as the main concepts of quantum information theory.|
|Objective||It is the goal of this course to get familiar with the most important notions that are of importance for the connection between Information and Physics. The formalism of Quantum Physics will be motivated and derived, and the use of these laws for information processing will be understood. In particular, the important algorithms of Grover as well as Shor will be studied and analyzed.|
|Content||According to Landauer, "information is physical". In quantum information, one is interested in the consequences and the possibilites offered by the laws of quantum physics for information processing. Followed by an introduction to the basic principles of quantum physics, such as superposition, interference, or entanglement, a variety of subjects are treated: Quantum algorithms, teleportation, quantum communication complexity and "pseude-telepathy", quantum cryptography, as well as the main concepts of quantum information theory.|
|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.|
|263-4110-00L||Interdisciplinary Algorithms Lab |
In the Master Programme max. 10 credits can be accounted by Labs on top of the Interfocus Courses. Additional Labs will be listed on the Addendum.
|W||5 credits||2P||A. Steger, D. Steurer, J. Lengler|
|Abstract||In this course students will develop solutions for algorithmic problems posed by researchers from other fields.|
|Objective||Students will learn that in order to tackle algorithmic problems from an interdisciplinary or applied context one needs to combine a solid understanding of algorithmic methodology with insights into the problem at hand to judge which side constraints are essential and which can be loosened.|
|Prerequisites / Notice||Students will work in teams. Ideally, skills of team members complement each other. |
Interested Bachelor students can apply for participation by sending an email to email@example.com explaining motivation and transcripts.
|263-4310-00L||Linear Algebra Methods in Combinatorics||W||5 credits||2V + 2U||P. Penna|
|Abstract||This course describes the linear algebra bound technique also called dimension argument. To learn the technique we discuss several examples in combinatorics, geometry, and computer science. Besides this technique, the course aims at showing the mathematical elegance of certain proofs and the simplicity of the statements.|
|Objective||Becoming familiar with the method and being able to apply it to problems similar to those encountered during the course.|
|Content||This course is (essentially) about one single technique called the "linear algebra bound" (also known as "dimension argument"). We shall see several examples in combinatorics, geometry, and computer science and learn the technique throughout these examples. Towards the end of the course, we shall see the power of this method in proving rather amazing results (e.g., a circuit complexity lower bound, explicit constructions of Ramsey graphs, and a famous conjecture in geometry disproved). The course also aims at illustrating the main ideas behind the proofs and how the various problems are in fact connected to each other.|
|Lecture notes||Lecture notes of each single lecture will be made available (shortly after the lecture itself).|
|Literature||Most of the material of the course is covered by the following book:|
1. Linear algebra methods in combinatorics, by L. Babai and P. Frankl, Department of Computer Science, University of Chicago, preliminary version, 1992.
Some parts are also taken from
2. Extremal Combinatorics (with Applications in Computer Science), by Stasys Jukna, Springer-Verlag 2001.
|263-4312-00L||Advanced Data Structures||W||5 credits||2V + 2U||P. Uznanski|
|Abstract||Data structures play a central role in modern computer science and are essential building blocks in obtaining efficient algorithms. The course covers major results and research directions in data structures, that (mostly) have not yet made it into standard computer science curriculum.|
|Objective||Learning modern models of computation. Applying new algorithmic techniques to the construction of efficient data structures. Understanding techniques used in both lower- and upper- bound proofs on said data structures.|
|Content||This course will survey important developments in data structures that have not (yet) worked their way into the standard computer science curriculum. |
Though we will cover state of the art techniques, the presentation is relatively self-contained, and only assumes a basic undergraduate data structures course (e.g., knowledge of binary search trees).
The course material includes (but is not exhausted by):
- computation models and memory models
- string indexing (suffix trees, suffix arrays)
- search trees
- static tree processing (Lowest Common Ancestor queries, Level Ancestry queries)
- range queries on arrays (queries for minimal element in a given range)
- integers-only data structures: how to sort integers in linear time, faster predecessor structures (van Emde Boas trees)
- dynamic graphs connectivity
|Prerequisites / Notice||This is a highly theoretical course. You should be comfortable with:|
- algorithms and data structures
Completing Algorithms, Probability, and Computing course (252-0209-00L) is a good indicator.
|272-0301-00L||Methods for Design of Random Systems |
This course d o e s n o t include the Mentored Work Specialised Courses with an Educational Focus in Computer Science B.
|W||4 credits||2V + 1U||H.‑J. Böckenhauer, D. Komm, R. Kralovic|
|Abstract||The students should get a deep understanding of the notion of randomness and its usefulness. Using basic elements probability theory and number theory the students will discover randomness as a source of efficiency in algorithmic. The goal is to teach the paradigms of design of randomized algorithms.|
|Objective||To understand the computational power of randomness and to learn the basic|
methods for designing randomized algorithms
|Lecture notes||J. Hromkovic: Randomisierte Algorithmen, Teubner 2004.|
J.Hromkovic: Design and Analysis of Randomized Algorithms. Springer 2006.
J.Hromkovic: Algorithmics for Hard Problems, Springer 2004.
|Literature||J. Hromkovic: Randomisierte Algorithmen, Teubner 2004.|
J.Hromkovic: Design and Analysis of Randomized Algorithms. Springer 2006.
J.Hromkovic: Algorithmics for Hard Problems, Springer 2004.
|272-0302-00L||Approximation and Online Algorithms||W||4 credits||2V + 1U||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
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, blocks, 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||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||R. Weismantel|
|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,
- the theory of integral generating sets and its connection to totally dual integral systems,
- finite cutting plane algorithms based on lattices and integral generating sets.
|Lecture notes||not available, blackboard presentation|
|Literature||Bertsimas, Weismantel: Optimization over Integers, Dynamic Ideas 2005. |
Schrijver: Theory of linear and integer programming, Wiley, 1986.
|Prerequisites / Notice||"Mathematical Optimization" (401-3901-00L)|
|401-4904-00L||Combinatorial Optimization||W||6 credits||2V + 1U||R. Zenklusen|
|Abstract||Combinatorial Optimization deals with efficiently finding a provably strong solution among a finite set of options. This course discusses key combinatorial structures and techniques to design efficient algorithms for combinatorial optimization problems. We put a strong emphasis on polyhedral methods, which proved to be a powerful and unifying tool throughout combinatorial optimization.|
|Objective||The goal of this lecture is to get a thorough understanding of various modern combinatorial optimization techniques with an emphasis on polyhedral approaches. Students will learn a general toolbox to tackle a wide range of combinatorial optimization problems.|
|Content||Key topics include:|
- Polyhedral descriptions;
- Combinatorial uncrossing;
- Ellipsoid method;
- Equivalence between separation and optimization;
- Design of efficient approximation algorithms for hard problems.
|Lecture notes||Lecture notes will be available online.|
|Literature||- Bernhard Korte, Jens Vygen: Combinatorial Optimization. 5th edition, Springer, 2012.|
- Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency, Springer, 2003. This work has 3 volumes.
|Prerequisites / Notice||Prior exposure to Linear Programming can greatly help the understanding of the material. We therefore recommend that students interested in Combinatorial Optimization get familiarized with Linear Programming before taking this lecture.|
|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||4 credits||2V + 1U||J. Hromkovic|
|Abstract||This course unit looks into algorithmic approaches to the solving of hard problems. 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.|
|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.|
|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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