Suchergebnis: Katalogdaten im Frühjahrssemester 2023
Informatik Master  | ||||||||||||||||||||||||||||||||||||
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| Ergänzung in Theoretical Computer Science | ||||||||||||||||||||||||||||||||||||
| Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |||||||||||||||||||||||||||||||
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| 252-0408-00L | Cryptographic Protocols | W | 6 KP | 2V + 2U + 1A | M. Hirt | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | In a cryptographic protocol, a set of parties wants to achieve some common goal, while some of the parties are dishonest. Most prominent example of a cryptographic protocol is multi-party computation, where the parties compute an arbitrary (but fixed) function of their inputs, while maintaining the secrecy of the inputs and the correctness of the outputs even if some of the parties try to cheat. | |||||||||||||||||||||||||||||||||||
| Lernziel | To know and understand a selection of cryptographic protocols and to be able to analyze and prove their security and efficiency. | |||||||||||||||||||||||||||||||||||
| Inhalt | The selection of considered protocols varies. Currently, we consider multi-party computation, secret-sharing, broadcast and Byzantine agreement. We look at both the synchronous and the asynchronous communication model, and focus on simple protocols as well as on highly-efficient protocols. | |||||||||||||||||||||||||||||||||||
| Skript | We provide handouts of the slides. For some of the topics, we also provide papers and/or lecture notes. | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | A basic understanding of fundamental cryptographic concepts (as taught for example in the course Information Security) is useful, but not required. | |||||||||||||||||||||||||||||||||||
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| 252-1424-00L | Models of Computation | W | 6 KP | 2V + 2U + 1A | M. Cook | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | 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. | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Inhalt | 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. | |||||||||||||||||||||||||||||||||||
| 261-5110-00L | Optimization for Data Science | W | 10 KP | 3V + 2U + 4A | B. Gärtner, N. He | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course provides an in-depth theoretical treatment of optimization methods that are relevant in data science. | |||||||||||||||||||||||||||||||||||
| Lernziel | Understanding the guarantees and limits of relevant optimization methods used in data science. Learning theoretical paradigms and techniques to deal with optimization problems arising in data science. | |||||||||||||||||||||||||||||||||||
| Inhalt | This course provides an in-depth theoretical treatment of classical and modern optimization methods that are relevant in data science. After a general discussion about the role that optimization has in the process of learning from data, we give an introduction to the theory of (convex) optimization. Based on this, we present and analyze algorithms in the following four categories: first-order methods (gradient and coordinate descent, Frank-Wolfe, subgradient and mirror descent, stochastic and incremental gradient methods); second-order methods (Newton and quasi Newton methods); non-convexity (local convergence, provable global convergence, cone programming, convex relaxations); min-max optimization (extragradient methods). The emphasis is on the motivations and design principles behind the algorithms, on provable performance bounds, and on the mathematical tools and techniques to prove them. The goal is to equip students with a fundamental understanding about why optimization algorithms work, and what their limits are. This understanding will be of help in selecting suitable algorithms in a given application, but providing concrete practical guidance is not our focus. | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | A solid background in analysis and linear algebra; some background in theoretical computer science (computational complexity, analysis of algorithms); the ability to understand and write mathematical proofs. | |||||||||||||||||||||||||||||||||||
| 263-4400-00L | Advanced Graph Algorithms and Optimization | W | 10 KP | 3V + 3U + 3A | R. Kyng, M. Probst | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course will cover a number of advanced topics in optimization and graph algorithms. | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Inhalt | 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. | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | 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. | |||||||||||||||||||||||||||||||||||
| 263-4508-00L | Algorithmic Foundations of Data Science | W | 10 KP | 3V + 2U + 4A | D. Steurer | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course provides rigorous theoretical foundations for the design and mathematical analysis of efficient algorithms that can solve fundamental tasks relevant to data science. | |||||||||||||||||||||||||||||||||||
| Lernziel | We consider various statistical models for basic data-analytical tasks, e.g., (sparse) linear regression, principal component analysis, matrix completion, community detection, and clustering. Our goal is to design efficient (polynomial-time) algorithms that achieve the strongest possible (statistical) guarantees for these models. Toward this goal we learn about a wide range of mathematical techniques from convex optimization, linear algebra (especially, spectral theory and tensors), and high-dimensional statistics. We also incorporate adversarial (worst-case) components into our models as a way to reason about robustness guarantees for the algorithms we design. | |||||||||||||||||||||||||||||||||||
| Inhalt | Strengths and limitations of efficient algorithms in (robust) statistical models for the following (tentative) list of data analysis tasks: - (sparse) linear regression - principal component analysis and matrix completion - clustering and Gaussian mixture models - community detection | |||||||||||||||||||||||||||||||||||
| Skript | To be provided during the semester | |||||||||||||||||||||||||||||||||||
| Literatur | High-Dimensional Statistics A Non-Asymptotic Viewpoint by Martin J. Wainwright | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Mathematical and algorithmic maturity at least at the level of the course "Algorithms, Probability, and Computing". Important: Optimization for Data Science 2018--2021 This course was created after a reorganization of the course "Optimization for Data Science" (ODS). A significant portion of the material for this course has previously been taught as part of ODS. Consequently, it is not possible to earn credit points for both this course and ODS as offered in 2018--2021. This restriction does not apply to ODS offered in 2022 or afterwards and you can earn credit points for both courses in this case. | |||||||||||||||||||||||||||||||||||
| 263-4509-00L | Complex Network Models | W | 5 KP | 2V + 2A | J. Lengler | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | Complex network models are random graphs that feature one or several properties observed in real-world networks (e.g., social networks, internet graph, www). Depending on the application, different properties are relevant, and different complex network models are useful. This course gives an overview over some relevant models and the properties they do and do not cover. | |||||||||||||||||||||||||||||||||||
| Lernziel | The students get familiar with a portfolio of network models, and they know their features and shortcomings. For a given application, they can identify relevant properties for this applications and can select an appropriate network model. | |||||||||||||||||||||||||||||||||||
| Inhalt | Network models: Erdös-Renyi random graphs, Chung-Lu graphs, configuration model, Kleinberg model, geometric inhomogeneous random graphs Properties: degree distribution, structure of giant and smaller components, clustering coefficient, small-world properties, community structures, weak ties | |||||||||||||||||||||||||||||||||||
| Skript | The script is available in moodle or at https://as.inf.ethz.ch/people/members/lenglerj/CompNetScript.pdf It will be updated during the semester. | |||||||||||||||||||||||||||||||||||
| Literatur | Latora, Nikosia, Russo: "Complex Networks: Principles, Methods and Applications" van der Hofstad: "Random Graphs and Complex Networks. Volume 1" | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | The students must be familiar with the basics of graph theory and of probability theory (e.g. linearity of expectation, inequalities of Markov, Chebyshev, Chernoff). The course "Randomized Algorithms and Probabilistic Methods" is helpful, but not required. | |||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 263-4510-00L | Introduction to Topological Data Analysis | W | 8 KP | 3V + 2U + 2A | P. Schnider | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | Topological Data Analysis (TDA) is a relatively new subfield of computer sciences, which uses techniques from algebraic topology and computational geometry and topology to analyze and quantify the shape of data. This course will introduce the theoretical foundations of TDA. | |||||||||||||||||||||||||||||||||||
| Lernziel | The goal is to make students familiar with the fundamental concepts, techniques and results in TDA. At the end of the course, students should be able to read and understand current research papers and have the necessary background knowledge to apply methods from TDA to other projects. | |||||||||||||||||||||||||||||||||||
| Inhalt | Mathematical background (Topology, Simplicial complexes, Homology), Persistent Homology, Complexes on point clouds (Čech complexes, Vietoris-Rips complexes, Delaunay complexes, Witness complexes), the TDA pipeline, Reeb Graphs, Mapper | |||||||||||||||||||||||||||||||||||
| Literatur | Main reference: Tamal K. Dey, Yusu Wang: Computational Topology for Data Analysis, 2021 https://www.cs.purdue.edu/homes/tamaldey/book/CTDAbook/CTDAbook.html Other references: Herbert Edelsbrunner, John Harer: Computational Topology: An Introduction, American Mathematical Society, 2010 https://bookstore.ams.org/mbk-69 Gunnar Carlsson, Mikael Vejdemo-Johansson: Topological Data Analysis with Applications, Cambridge University Press, 2021 Link Robert Ghrist: Elementary Applied Topology, 2014 https://www2.math.upenn.edu/~ghrist/notes.html Allen Hatcher: Algebraic Topology, Cambridge University Press, 2002 https://pi.math.cornell.edu/~hatcher/AT/ATpage.html | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | The course assumes knowledge of discrete mathematics, algorithms and data structures and linear algebra, as supplied in the first semesters of Bachelor Studies at ETH. | |||||||||||||||||||||||||||||||||||
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| 263-4656-00L | Digital Signatures | W | 5 KP | 2V + 2A | D. Hofheinz | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | 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. | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Inhalt | 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. | |||||||||||||||||||||||||||||||||||
| Literatur | Jonathan Katz, "Digital Signatures." | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Ideally, students will have taken the D-INFK Bachelors course "Information Security" or an equivalent course at Bachelors level. | |||||||||||||||||||||||||||||||||||
| 272-0300-00L | Algorithmik für schwere Probleme Diese Lerneinheit beinhaltet die Mentorierte Arbeit Fachwissenschaftliche Vertiefung mit pädagogischem Fokus Informatik A n i c h t ! | W | 5 KP | 2V + 1U + 1A | H.‑J. Böckenhauer, D. Komm | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | Diese Lerneinheit beschäftigt sich mit algorithmischen Ansätzen zur Lösung schwerer Probleme, insbesondere mit exakten Algorithmen mit moderat exponentieller Laufzeit und parametrisierten Algorithmen. Eine umfassende Reflexion über die Bedeutung der vorgestellten Ansätze für den Informatikunterricht an Gymnasien begleitet den Kurs. | |||||||||||||||||||||||||||||||||||
| Lernziel | Auf systematische Weise eine Übersicht über die Methoden zur Lösung schwerer Probleme kennen lernen. Vertiefte Kenntnisse im Bereich exakter und parameterisierter Algorithmen erwerben. | |||||||||||||||||||||||||||||||||||
| Inhalt | Zuerst wird der Begriff der Berechnungsschwere erläutert (für die Informatikstudierenden wiederholt). Dann werden die Methoden zur Lösung schwerer Probleme systematisch dargestellt. Bei jeder Algorithmenentwurfsmethode wird vermittelt, was sie uns garantiert und was sie nicht sichern kann und womit wir für die gewonnene Effizienz bezahlen. Ein Schwerpunkt liegt auf exakten Algorithmen mit moderat exponentieller Laufzeit und auf parametrisierten Algorithmen. | |||||||||||||||||||||||||||||||||||
| Skript | Unterlagen und Folien werden zur Verfügung gestellt. | |||||||||||||||||||||||||||||||||||
| Literatur | 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 | Approximations- und Online-Algorithmen Findet dieses Semester nicht statt. | W | 5 KP | 2V + 1U + 1A | D. Komm | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | Diese Lerneinheit behandelt approximative Verfahren für schwere Optimierungsprobleme und algorithmische Ansätze zur Lösung von Online-Problemen sowie die Grenzen dieser Ansätze. | |||||||||||||||||||||||||||||||||||
| Lernziel | Auf systematische Weise einen Überblick über die verschiedenen Entwurfsmethoden von approximativen Verfahren für schwere Optimierungsprobleme und Online-Probleme zu gewinnen. Methoden kennenlernen, die Grenzen dieser Ansätze aufweisen. | |||||||||||||||||||||||||||||||||||
| Inhalt | Approximationsalgorithmen sind einer der erfolgreichsten Ansätze zur Behandlung schwerer Optimierungsprobleme. Dabei untersucht man die sogenannte Approximationsgüte, also das Verhältnis der Kosten einer berechneten Näherungslösung und der Kosten einer (nicht effizient berechenbaren) optimalen Lösung. Bei einem Online-Problem ist nicht die gesamte Eingabe von Anfang an bekannt, sondern sie erscheint stückweise und für jeden Teil der Eingabe muss sofort ein entsprechender Teil der endgültigen Ausgabe produziert werden. Die Güte eines Algorithmus für ein Online-Problem misst man mit der competitive ratio, also dem Verhältnis der Kosten der berechneten Lösung und der Kosten einer optimalen Lösung, wie man sie berechnen könnte, wenn die gesamte Eingabe bekannt wäre. Inhalt dieser Lerneinheit sind - die Klassifizierung von Optimierungsproblemen nach der erreichbaren Approximationsgüte, - systematische Methoden zum Entwurf von Approximationsalgorithmen (z. B. Greedy-Strategien, dynamische Programmierung, LP-Relaxierung), - Methoden zum Nachweis der Nichtapproximierbarkeit, - klassische Online-Probleme wie Paging oder Scheduling-Probleme und Algorithmen zu ihrer Lösung, - randomisierte Online-Algorithmen, - Entwurfs- und Analyseverfahren für Online-Algorithmen, - Grenzen des "competitive ratio"- Modells und Advice-Komplexität als eine Möglichkeit, die Komplexität von Online-Problemen genauer zu messen. | |||||||||||||||||||||||||||||||||||
| Literatur | Die Vorlesung orientiert sich teilweise an folgenden Büchern: J. Hromkovic: Algorithmics for Hard Problems, Springer, 2004 D. Komm: An Introduction to Online Computation: Determinism, Randomization, Advice, Springer, 2016 Zusätzliche Literatur: 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 KP | 4V + 1U | B. Sudakov | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | 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 | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Skript | Lecture will be only at the blackboard. | |||||||||||||||||||||||||||||||||||
| Literatur | West, D.: "Introduction to Graph Theory" Diestel, R.: "Graph Theory" Further literature links will be provided in the lecture. | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | 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 KP | 3G | R. Zenklusen | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | 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. | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Inhalt | Key topics include: - Matching problems; - Integer Programming techniques and models; - Extended formulations and strong problem formulations; - Solver techniques for (Mixed-)Integer Programs; - Decomposition approaches. | |||||||||||||||||||||||||||||||||||
| Literatur | - 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. | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | 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 Dieser theoretisch ausgerichtete Teil QIP I bildet zusammen mit dem experimentell ausgerichteten Teil 402-0448-02L QIP II, die beide im Frühjahrssemester angeboten werden, im Master-Studiengang Physik das experimentelle Kernfach "Quantum Information Processing" mit total 10 ECTS-Kreditpunkten. | W | 5 KP | 2V + 1U | J. Home | |||||||||||||||||||||||||||||||
| Kurzbeschreibung | 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. | |||||||||||||||||||||||||||||||||||
| Lernziel | 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. | |||||||||||||||||||||||||||||||||||
| Inhalt | 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. | |||||||||||||||||||||||||||||||||||
| Skript | Will be provided. | |||||||||||||||||||||||||||||||||||
| Literatur | Quantum Computation and Quantum Information Michael Nielsen and Isaac Chuang Cambridge University Press | |||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | A good understanding of finite dimensional linear algebra is recommended. | |||||||||||||||||||||||||||||||||||
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