IA062 Randomized Algorithms and Computations

Faculty of Informatics
Autumn 2023
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Daniel Kráľ, Ph.D., DSc. (lecturer)
Mgr. Daniel Iľkovič (seminar tutor)
prof. RNDr. Daniel Kráľ, Ph.D., DSc. (seminar tutor)
Marcin Briański (assistant), prof. RNDr. Daniel Kráľ, Ph.D., DSc. (deputy)
Guaranteed by
prof. RNDr. Daniel Kráľ, Ph.D., DSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Tue 8:00–9:50 A217
  • Timetable of Seminar Groups:
IA062/01: Wed 8:00–9:50 A218, D. Iľkovič, D. Kráľ
Prerequisites
General algorithmic and mathematical knowledge is expected.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim: randomized algorithms and methods are becoming one of the key tools for an effective solution of a variety of problems in informatics and its aplications practically in all theoretical and aplication areas.
Learning outcomes
After finishing the lecture student will be able: To manage basic techniques to design randomized algorithms; to understand differences concerning power of deterministic and randomized algorithms; to manage basic tools for analysis of randomized algorithms; to work with tail inequalities; to understand power and use of the probabilistic method; to understand power of random walks; to understand power of randomized proofs; to understand basic principles of randomized cryptographic protocols.
Syllabus
  • Randomized algorithms and methods.
  • Examples of randomized algorithms.
  • Methods of game theory.
  • Main types of randomized algorithms.
  • Randomized complexity classes.
  • Chernoff's bounds.
  • Moments and deviations.
  • Probabilistic methods.
  • Markov chains and random walks.
  • Algebraic methods.
  • Aplications:
  • Linear programming.
  • Parallel and distributed algoritms.
  • Randomization in cryptography.
  • Randomized methods in theory of numbers.
Literature
    recommended literature
  • MOTWANI, Rajeev and Prabhakar RAGHAVAN. Randomized algorithms. Cambridge: Cambridge University Press, 1995, xiv, 476. ISBN 0521474655. info
Teaching methods
IA062 is taught in weekly 2-hour lectures accompanied by 2-hour tutorials.
Assessment methods
The resulting grade will based on the final oral exam.
Language of instruction
English
Further Comments
Study Materials
The course is taught annually.
Teacher's information
https://www.fi.muni.cz/~dkral/ia062.html
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2023/IA062