LTI
LTI

Randomized Algorithms

General Info

  • Lecturer: Prof. Dr. Susanne Albers
  • Module: IN2160 TUMonline
  • Area:
    4+2 lectures per week in area III (Theoretical Computer Science)
    core course, topic algorithms
  • Time and Place:
    Monday, 10:00 – 12:00, 00.13.009A
    Wednesday, 8:00 – 10:00, 00.13.009A
  • Exercises (web page):
    2 hours per week exercises accompanying the lectures
    Date TBA
  • Course Certificate:
    To successfully complete the module students must obtain at least 50% of the points in the written exam. A bonus of 0.3 in the final grade will be granted if students achieve at least 50% of the points in the homework assignments.
  • Audience:
    graduate students of computer science
    students with computer science as minor
  • Prerequisites:
    1st and 2nd year courses
    Efficient Algorithms and Data Structures is beneficial but not mandatory.
  • Recommended for:
    Extended knowledge in topic Algorithms

Announcements

There will be no class on October 12, 2015 as that day is Dies Academicus.

Content

Over the past 25 years the design and analysis of randomized algorithms, which make random choices during their execution, has become an integral part of algorithm theory. For many problems, surprisingly elegant and fast randomized algorithms can be developed. In this lecture we will (a) study basic tools from probability theory needed in probabilistic analyses and (b) design randomized algorithms for a number of fundamental problems.

  • October 14, 2015 (two lectures): Basic results; randomized quicksort; min-cut algorithm; [MR] pages 3-8.
  • October 19, 2015: Basic results; min-cut algorithm conitnued; binary planar partitions; [MR] pages 8-11.
  • October 21, 2015: Basic results; binary planar partitions continued; [MR] pages 13-14.
  • October 26, 2015: Basic results; verifying matrix multiplication; a probabilistic recurrence; [MU] pages 8-10 and [MR] page 15 and 21-22.
  • October 28, 2015: Basic results; a probabilistic recurrence continued; complexity classes; [MR] pages 15, 16 and 21.
  • November 2, 2015: Basic results; complexity classes; Game-theoretic techniques; game tree evaluation; [MR] pages 22-23 and 28.
  • November 4, 2015: Game-theoretic techniques; game tree evaluation, von Neumann's minimax theorem; [MR] pages 29-31.
  • November 9, 2015: Game-theoretic techniques; von Neumann's minimax theorem continued; Yao's technique; [MR] pages 32-35.
  • November 11, 2015: Game-theoretic techniques; Yao's technique continued; a lower bound for game tree evaluation; [MR] pages 35-37.
  • November 16, 2015: Game-theoretic techniques; randomness and non-uniformity; [MR] pages 38-40.
  • November 18, 2015: Moments and deviations; occupancy problems; [MR] pages 43-45.
  • November 23, 2015: Moments and deviations; bucket sort; inequalities by Markov and Chebyshev; [MU] page 94 and [MR] pages 45-47.
  • November 25, 2015: Moments and deviations; median algorithm; [MU] pages 53-56.
  • November 30, 2015: Moments and deviations; median algorithm continued; two-point sampling; [MU] pages 56-57 and [MR] pages 51-52, .
  • December 2, 2015: Moments and deviations; two-point sampling continued; coupon collector's problem; [MR] pages 52-53, and [MU] pages 33 and 50-52.
  • December 7, 2015: Moments and deviations; stable marriage problem, [MR] pages 53-57. Chernoff bounds; moment generating functions; [MU] page 61.
  • December 9, 2015: Chernoff bounds; moment generating functions; deriving Chernoff bounds; bounds for Poisson trials; [MU] page 62-66.
  • December 14, 2015: Chernoff bounds; coin flips; parameter estimation; a better bound for a special case; set balancing; [MU] pages 67-72.
  • December 16, 2015: Chernoff bounds; packet routing on the hypercube; [MU] pages 72-75.
  • December 21, 2015 (two lectures): Chernoff bounds; packet routing on the hypercube; a wiring problem; [MU] pages 75-78 and [MR] pages 79-82.
  • January 11, 2016: The probabilistic method; the basic counting argument; the expectation argument; [MU] page 126-130.
  • January 13, 2016: The probabilistic method; the expectation argument; sample and modify; [MU] pages 130-132.
  • January 18, 2016: The probabilistic method; sample and modify; Data structures; treaps; [MU] page 133 and [MR] 201-208.
  • January 20, 2016: Data structures; treaps; [MR] 201-208.
  • January 25, 2016: Data structures; treaps; [MR] 201-208.
  • January 27, 2016: Data structures; universal hashing; [MR] 216-220.
  • February 1, 2016: Data structures; perfect hashing; [MU] 326-328 and [MR] 221-229.

Literature

  • [MU] M. Mitzenmacher and E. Upfal. Probability and Computing: Randomized Algorithms and ProbabilisticAnalysis. Cambridge University Press, 2005.
  • [MR] R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.

December 2017: Susanne Albers will give keynote address at the Graduation Day, Department of Computer Science at RWTH Aachen University.

ESA/ALGO 2019 will be organized by Susanne Albers and her group.

April 2017: New Research Training Center AdONE, funded by the German Research Foundation.

Susanne Albers receives ERC Advanced Grant. Press release of the Bavarian State Ministry of the Sciences, Research and the Arts.

August 2016: Susanne Albers is keynote speaker at Euro-Par 2016, Grenoble.

Susanne Albers, Nicole Megow and Andreas S. Schulz will organize MAPSP 2017.

Juni 2016: Susanne Albers gives an invited lecture at the Academy of Sciences and Literature, Mainz.

September 2015: Susanne Albers is invited speaker at MPI-INF – 25th Anniversary. The program features several Turing Award winners, Leibniz Prize winners, Humboldt Prize winners and ERC Grant winners.

June 2015: Susanne Albers is keynote speaker at the 31st International Symposium on Computational Geometry (SOCG15), Eindhoven.

June 2015: Susanne Albers is invited speaker of the tutorial on Network Creation Games: How Does the Internet Form? organized by Erik D. Demaine (MIT) and MohammadTaghi Hajiaghayi (University of Maryland). 16th Conference on Electronic Commerce (EC15), Portland, Oregon.

Lehrstuhl für Theoretische Informatik
Prof. Dr. Susanne Albers

Boltzmannstr. 3
85748 Garching bei München

Tel +89.289.17706
Fax +89.289.17707

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