IA062 Randomized Algorithms and Computations

Faculty of Informatics
Spring 2014
Extent and Intensity
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. Jozef Gruska, DrSc. (lecturer)
RNDr. Mgr. Jana Dražanová, Ph.D. (seminar tutor)
Shenggen Zheng, PhD (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Jozef Gruska, DrSc.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Wed 10:00–11:50 B410, Wed 18:00–19:50 D2
Prerequisites
Basic knowledge from algebra, probability as well as design and analysis of algorithms
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
there are 18 fields of study the course is directly associated with, display
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. 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 and concentration bounds; to understand power and use of the probabilistic method; to understand power of random walks and Markov chain and Lovasz Lemma to understand power of randomized proofs; to understand concept of martingales to understand basic principles of randomized cryptographic protocols.
Syllabus
  • Introduction, basic methods to design randomized algorithms
  • Examples of randomized algorithms.
  • Methods of game theory for analysis of randomized algorithms.
  • Main types of randomized algorithms.
  • Randomized complexity classes.
  • Chernoff's bounds and concentration bounds
  • Moments and deviations. Martingales
  • Probabilistic method and its use. Lovasz lemma
  • Markov chains and random walks. Metropolis algorithm
  • Randomization in cryptography.
  • Randomized methods in theory of numbers and in algebra
  • Randomized proofs
  • Quantum algorithms
Literature
  • GRUSKA, Jozef. Foundations of computing. London: International Thompson Computer Press, 1997, xv, 716 s. ISBN 1-85032-243-0. info
  • MOTWANI, Rajeev and Prabhakar RAGHAVAN. Randomized algorithms. Cambridge: Cambridge University Press, 1995, xiv, 476. ISBN 0521474655. info
Teaching methods
lectures
Assessment methods
oral exam
Language of instruction
English
Further Comments
Study Materials
The course is taught annually.
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 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Autumn 2023.
  • Enrolment Statistics (Spring 2014, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2014/IA062