- Wed Apr 23:
I have reserved Bell 242 9-12 for the entire week of next week (starting
Apr 28) for the final presentations. We will have 2 presentations each
day. Each presentation will take roughly 1 hour (give and take, plus a few
minutes for questions).
The presentation order is as follows.
- Monday, Apr 28, 9am:
- Xin Liu: Energy Efficient randomized communication in unknown ad hoc networks.
- Hung Ngo: Finding Disjoint Paths in Expanders Deterministically and On-Line
- Tuesday, 9am
- Thanh-Nhan Nguyen:
- Steve Uurtamo:
- Wednesday, 9am:
- Madhavi Nadig: On certain connectivity properties of the Internet topology
- Abhijth Kashyap: Why Simple Hash Functions Work: Exploiting the Entropy in a Data Stream
- Thursday, 9am
- Demian Lessa: The Power of One Move: Hashing Scheme for Hardware
- Abhishek Murthy: Estimating the Sortedness of Data Stream
- Friday, 9am
- Ying Liu: The Cover Time of Random Digraphs
- Venkatasairam Yanamandram: Balanced Allocations: The Heavily Loaded Case
- Monday, Apr 28, 9am:
- Mon Mar 31: lecture notes on approximate counting, Monte Carlo Method uploaded. The basics are there, few more examples will be updated in a week or so.
- Mon Mar 24: lecture notes on applications of MC updated. Discussions on expanders is complete, I hope.
- Mon Mar 24: there will be no class on Wed Mar 26 due to the graduate conference.
- Mon Mar 17: assignment 4 is posted. Due on Monday Apr 07. This is the last assignment!
- Mon Mar 17: (incomplete) notes for random walks and expanders uploaded
- Sun Mar 16: Final Presentation Paper Assignments.
- A Note on the Presentations:
- Please prepare slides.
- It is preferable if you use LaTeX Beamer. PPT is ok but looks very ugly. I have a set of presentation slides from my first lecture prepared using Beamer, which you should make use of as a template. Note the following:
- Type "make" will produce main.pdf which could be viewed with acroread or xpdf. xpdf is prefered while preparing the slides since xpdf automatically refreshes when you "make" again. (Just go to the previous page and back, and the file is reloaded.)
- When producing the final slides, do "make" twice in a row, or "pdflatex main" twice in a row. This makes sure the the table of content and cross-references are correctly constructed and
- If
you do include graphics, use the "includegraphics" command as in the
template. Most graphic types are ok: pdf, jpeg, png, etc., except for
eps/ps which you'll have to convert to pdf before inclusion.
- Please follow roughly the following outline in the presentation:
- What's the problem
- What are the related works to date (of the paper)
- What's the main line of attack, i.e. outline the key lemmas and theorems (before proving them)
- Try to explain in English the main ideas behind the lemmas and theorems
- Finally, prove some of them as time allows. Skip calculus or elementary details.
- Let us know what you think
might be next in terms of open problems, things you might try, etc.
- Abhijith Ramesh Kashyap:
- Michael Mitzenmacher and Salil Vadhan, Why Simple Hash Functions Work: Exploiting the Entropy in a Data Stream, SODA 2008
- Demian Lessa:
- A. Kirsch and M. Mitzenmacher.The Power of One Move: Hashing Schemes for Hardware. INFOCOM 2008.
- Xin Liu:
- Petra Berenbrink, Colin Cooper, Zengjian Hu: Energy efficient randomised communication in unknown AdHoc networks. SPAA 2007: 250-259
- Ying Liu:
- Colin Cooper, Alan M. Frieze: The Cover Time of Random Digraphs. APPROX-RANDOM 2007: 422-435
- Abhishek Murthy:
- Gopalan, Jayram, Krauthgamer, Estimating the Sortedness of Data Streams, SODA 2007
- Madhavi Nadig:
- Mihail, M.; Papadimitriou, C.; Saberi, A.; On certain connectivity properties of the Internet topology, FOCS 2003 11-14 Oct. 2003 Page(s):28 - 35
- Thanh-Nhan Nguyen:
- Constantinos Daskalakis, Alexandros G. Dimakis, Richard M. Karp, and Martin J. Wainwright, Probabilistic Analysis of Linear Programming Decoding, SODA 2007.
- Steve Uurtamo:
- Achlioptas, D. and Peres, Y. 2003. The threshold for random k-SAT is 2k (ln 2 - O(k)). STOC '03.
- Venkatasairam Yanamandram:
- Aravind Srinivasan, Improved Algorithmic Versions of Lovasz Local Lemma, SODA 2008
- Other Choices of Papers: (these are the ones I am personally interested in, you can choose to present one of them instead of the assigned paper. I will try to update this list of optional papers in the next week so that you'll ... feel like you have more choices!)
- N. Alon and M. Capalbo, Finding disjoint paths in expanders deterministically and online, Proc. of the 48th IEEE FOCS,
- N. Alon, A. Andoni, T. Kaufman, K. Matulef, R. Rubinfeld and N. Xie, Testing k-wise and Almost k-wise Independence, Proc. of the 39 ACM STOC, 496-505.
- N. Alon, O. Schwartz and A. Shapira, An elementary construction of constant-degree expanders, SODA 2007
- N. Alon, D. Moshkovitz and M. Safra, Algorithmic construction of sets for k-restrictions, ACM Transactions on Algorithms 2 (2006), 153-177.
- Petra Berenbrink, Artur Czumaj, Angelika Steger, Berthold Vöcking: Balanced Allocations: The Heavily Loaded Case. SIAM J. Comput. 35(6): 1350-1385 (2006)
- Alan M. Frieze: Perfect matchings in random bipartite graphs with minimal degree at least 2. Random Struct. Algorithms 26(3): 319-358 (2005)
- Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, Eric Vigoda: Randomly Coloring Constant Degree Graphs. FOCS 2004: 582-589
- Jayram, Kale, Vee, Efficient Aggregation Algorithms for Probabilistic Data, SODA 2007.
- Thomas P. Hayes, Juan C. Vera, Eric Vigoda: Randomly coloring planar graphs with fewer colors than the maximum degree. STOC 2007: 450-458
- Michael Alekhnovich, Eli Ben-Sasson, Linear Upper Bounds for Random Walk on Small Density Random 3-CNF, FOCS 2003: 352-361
- Vöcking, B. 2001. Almost optimal permutation routing on hypercubes. STOC 2001. 530-539.
- Wed, Mar 05: solution to assignment 2 has been posted.
- Wed, Feb 27: Chapter 1 from a book by James Norris is perhaps one of the best free resources on the Net about DTMC. My presentation roughly follows his chapter.
- Wed, Feb 27: Homework assignment 3 is posted. Due on Monday March 17.
- Sat, Feb 23:
- Notes on DTMC updated. More or less complete. Please reprint even the covered slides since I reorganized some slides.
- Sun, Feb 17:
- Lecture notes on the probabilistic method is now completed and uploaded.
- Partial notes on discrete time markov chains is also uploaded.
- Tue, Feb 12: (Partial) lecture notes on the probabilistic method updated. The Second Moment Method is included. The Lovasz Local Lemma will be updated in the next few days.
- Wed, Feb 06: (Partial) lecture notes on the probabilistic method uploaded.
- Tue, Feb 05: Solution to assignment 1 is posted. You'll need username/password to access it. I'll tell you tomorrow the U/P pair. If you're in a hurry to read the key, drop me an email.
- Mon, Feb 04: Assignment 2 is posted. Due in 3 weeks. Please start early. This is a little more demanding than the previous one. You've already known enough to solve all the problems.
- Fri, Feb 01: Lecture Note on Balls and Bins model has been uploaded.
- Wed, Jan 16: My office hours for the semester will be on Mondays and Wednesdays, 3-4pm. (Right after class.) Let me know if this does not work for you!
- Mon, Jan 14: Homework Assignment 1 is available. Due in 3 weeks!
- This is the space where announcements regarding the course shall be made throughout the semester.
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Probabilistic analysis and randomized algorithms have become an indispensible tool in virtually all areas of Computer Science, ranging from combinatorial optimization, machine learning, approximation algorithms analysis and designs, complexity theory, coding theory, to communication networks and secure protocols. This course has two major objectives: (a) it introduces key concepts, tools and techniques from probability theory which are often employed in the development of probabilistic algorithms and analyses and in the constructions of combinatorial objects, and (b) it gives a glance of how these concepts and techniques are used in algorithm analysis and design and combinatorial constructions, among other usages. In addition to the probabilistic paradigm, students are expected to gain substantial discrete mathematics problem solving skills essential for computer engineers. |
Prerequisites
CSE 531 or equivalence, good grasp of discrete mathematic thinking.. Rudimentary knowledge of discrete probability theory. |
Teaching staff and related info
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Required Textbook Michael Mitzenmacher and Eli Upfal, Probability and Computing, Cambridge University Press, 2005.
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Reference
books: helpful, but not required.
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