Randomized Algorithms (summer term 2014)
The course is given by Dr. Sabine Storandt. It takes place every Monday and Wednesday from 10:15am until 11:45am in the Hörsaal 03-26 in building 51.
Topics
- Las Vegas & Monte Carlo Algorithms
- Applications for Randomized Algorithms and Data Structures
- Improving Deterministic Bounds via Randomization
- Randomization in Games and AI
- Randomized Online Algorithms
- Probabilistic Method
Script
The complete script of the lecture (including some further references) is available in the course svn repository.
The final version (last change: 19.08.14) of the script can be viewed here.
Please report any kind of mistakes (grammar, spelling, content) via email. Content errors corrected after 29.07.2014 will be listed on this website for easy adaption of printed scripts.
@12.08.14: S.60 With the optimal cost being equal to αM , the resulting ratio is 1 + 2/α ====> the resulting ratio is 1 + 1/(2α)
@16.08.14: S.49 the sum of 2{i+1} from i=1 to j+1 is not 2(2 {j+2} -1) but 2(2 {j+2} -2), and in the same flavour the sum of 2{i+1} from i=1 to j is not 2(2 {j+1} -1) but 2(2 {j+1} -2)
@19.08.14: S.13 |A1 | ≥ k instead of |A1 | > k
@19.08.14: S.22 Lemma 2.12 |U | ≥ (n − 1) · m + 1 instead of |U | ≥ (n − 1) (m + 1)
Exam
The oral exam takes place at 26.08.2014.
Here is a list of example questions that are likely to be asked in the exam.
Question Time
==> Monday, 04.08. at 16:15 and Monday, 25.08. at 10:15 (Hörsaal 03-26 in building 51). Please come prepared, i.e. read through the script before and tell me explicitly what is unclear or where you need additional explanations.
Dates
1. Preliminaries
28.04. Introduction & Basic Stochastics notes
30.04. Las Vegas and Monte Carlo Algorithms: Analysis and Concentration Bounds, LV & MC for Max 3-SAT notes
2. Randomized Algorithms and Data Structures
05.05. k-Select, Approximative Median and Quick-Sort, Sorting Lower Bound notes
07.05. Sorting Lower Bounds continued, Deterministic & Randomized Skip-Listsnotes
12.05. Universal Hashingnotes
14.05. Exercise. Focus: Deterministic & Randomized Sorting notesexample code
19.05. Fingerprinting and Further Hashing Applications, Introduction to Samplingnotes
21.05. VC-dimension of Set Systems & Epsilon-Nets notes
26.05. Exercise + Good Random Samples for Systems with Small VC-dimension and Epsilon-Nets notes
02.06. Good Hitting Set Approximations notes
04.06. Route Planning and Epsilon-Nets notes
16.06. Exercise. Focus: Hitting Sets for Road Networksnotesexample code
3. Getting Beyond Deterministic Bounds via Randomization
18.06. The Closest Pair problemnotes
23.06. The Min Cut problemnotes
25.06. Sublinear Algorithmsnotes
30.06. Long Path problems + Exercise (Min Cut and Connected Components)notesexample code connected componentsexample code min cut
4. Randomization in AI
02.07. Exercise (Min Cut ctd. and Long Path) + The Cow Path Problem notes
07.07. Robot Navigation in Unknown Terrain: Deterministic Algorithmsnotes
09.07. Robot Navigation in Unknown Terrain: Randomized Algorithmnotes
14.07. Robot Navigation ctd., Competitive Bidding, Exercise: Cows & Robotsnotes
5. Online Algorithms
6. Probabilistic Method
23.07. Lovasz Local Lemmanotes