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The complete script of the lecture (including further references) will be made available in the course svn repository. | The complete script of the lecture (including some further references) is available in the course svn repository. |
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The current version (last change: 12.05.14) of the script can be viewed [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/script.pdf|here.]] | The final version (last change: 20.08.14) of the script can be viewed [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/script.pdf|here.]] |
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(The list of contents may still change during the course of the lecture.) | 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. |
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{{{#!html <span style="color:red">*****IMPORTANT: if you plan to take the exam, please send me an email until 23.05. (the words exam and randomized algorithms should appear in the subject)*****</span> }}} |
@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) @20.08.14: S.39 P(n) >= (1 - 2/n) * P(n - 1) anstatt P(n) <= (1 - 2/n) * P(n - 1) @20.08.14: S.41 FastCut has to reduce the number of nodes down to (n+1)\sqrt(2) to make the success probability larger than 1/2, also the screw up probabilty missed the '1-' term at the beginning @20.08.14: S.49 The sum in Lemma 4.1 is n^2^+2n, not n^2^. |
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'''Exam''' The oral exam takes place at 26.08.2014. [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/questions.pdf|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. |
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1. Preliminaries | |
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2. Randomized Algorithms and Data Structures | |
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* 21.05. ''VC-dimension of Set Systems'' * 26.05. * 28.05. ''no lecture'' :( * 02.06. * 04.06. * 16.06. * 18.06. * 23.06. * 25.06. * 30.06. * 02.07. * 07.07. * 09.07. * 14.07. * 16.07. * 21.07. * 23.07. * 28.07. ''test exam'' * 30.07. ''test exam'' |
* 21.05. ''VC-dimension of Set Systems & Epsilon-Nets'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture8.pdf|notes]] * 26.05. ''Exercise + Good Random Samples for Systems with Small VC-dimension and Epsilon-Nets'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture9.pdf|notes]] * 02.06. ''Good Hitting Set Approximations'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture10.pdf|notes]] * 04.06. ''Route Planning and Epsilon-Nets'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture11.pdf|notes]] * 16.06. ''Exercise. Focus: Hitting Sets for Road Networks''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture12.pdf|notes]][[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Code/hit|example code]] 3. Getting Beyond Deterministic Bounds via Randomization * 18.06. ''The Closest Pair problem''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture13.pdf|notes]] * 23.06. ''The Min Cut problem''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture14.pdf|notes]] * 25.06. ''Sublinear Algorithms''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture15.pdf|notes]] * 30.06. ''Long Path problems + Exercise (Min Cut and Connected Components)''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture16.pdf|notes]][[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Code/cc|example code connected components]][[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Code/mincut|example code min cut]] 4. Randomization in AI * 02.07. ''Exercise (Min Cut ctd. and Long Path) + The Cow Path Problem'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture17.pdf|notes]] * 07.07. ''Robot Navigation in Unknown Terrain: Deterministic Algorithms''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture18.pdf|notes]] * 09.07. ''Robot Navigation in Unknown Terrain: Randomized Algorithm''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture19.pdf|notes]] * 14.07. ''Robot Navigation ctd., Competitive Bidding, Exercise: Cows & Robots''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture20.pdf|notes]] 5. Online Algorithms * 16.07. ''The Paging problem'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture21.pdf|notes]] * 21.07. ''Renting Skies and Buying a Bahn Card'' [[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture22.pdf|notes]] 6. Probabilistic Method * 23.07. ''Lovasz Local Lemma''[[https://daphne.informatik.uni-freiburg.de/svn-public/RandomizedAlgorithmsSS2014/public/lectures/Lecture23.pdf|notes]] |
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: 20.08.14) 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)
@20.08.14: S.39 P(n) >= (1 - 2/n) * P(n - 1) anstatt P(n) <= (1 - 2/n) * P(n - 1)
@20.08.14: S.41 FastCut has to reduce the number of nodes down to (n+1)\sqrt(2) to make the success probability larger than 1/2, also the screw up probabilty missed the '1-' term at the beginning
@20.08.14: S.49 The sum in Lemma 4.1 is n2+2n, not n2.
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