Probability and Algorithms, Caltech CS150, Fall 2016
Leonard J. Schulman
Schulman: CS150 2016
0.1
Syllabus
Class time: TR9:00-10:30 in Annenberg 314.
Office hours will normally be in my office, Annenberg 317. Just email to schedule an appointment. Ill
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Chapter 2
Algebraic Fingerprinting
There are several key ways in which randomness is used in algorithms. One is to push apart things
that are different even if they are similar. Well study a few examples of this phenomenon.
2.1
2.1.1
Lecture 5 (13/Oct): F
CHAPTER 1. SOME BASIC PROBABILITY THEORY
Schulman: CS150 2016
1.4
1.4.1
Lecture 4 (11/Oct): Clever applications of the probabilistic method
Large Girth and Large Chromatic Number (the deletion method)
Earlier we saw our first example of the probabilistic
Chapter 3
Concentration of Measure
3.1
3.1.1
Lecture 8 (25/Oct): Independent rvs, Chernoff bound, applications
Independent rvs
Lemma 30 If X1 , . . . , Xn are independent real rvs with finite expectations (recall this assumption requires that
the integral
CHAPTER 2. ALGEBRAIC FINGERPRINTING
Schulman: CS150 2016
2.2
2.2.1
Lecture 6 (18/Oct): Perfect Matchings
Matchings
A matching in a graph G = (V, E) is a set of vertex disjoint edges; the size of the matching is the
number of edges.
Let n = |V | and m = |
Chapter 5
Lovasz local lemma, applications and
algorithms
5.1
Lecture 17 (29/Nov): The Lovasz local lemma
The Lovasz local lemma is a fairly widely applicable tool for controlling the interactions among a large
collection of random variables.
Consider a p
CHAPTER 4. LIMITED INDEPENDENCE
Schulman: CS150 2016
4.4
4.4.1
Lecture 16 (22/Nov): Derandomization from small sample spaces
Derandomized MIS
We can achieve a similar result deterministically; that is, MIS is in NC. The key is that we can use
pairwise ind
Chapter 1
Some basic probability theory
1.1
1.1.1
Lecture 1 (27/Sep): some basic problems and definitions
Appetizers
1. You have aerial photographs of a country, with known scale. Estimate the total length of all
the roads.
2. N gentlemen check their hats
CHAPTER 3. CONCENTRATION OF MEASURE
Schulman: CS150 2016
3.4
Lecture 10 (1/Nov): Chernoff bound for general distributions.
Moment generating function. Start Johnson-Lindenstrauss
Now for a version of the Chernoff bound which we can apply to sums of indepe
Chapter 4
Limited independence
4.1
Lecture 13 (10/Nov): Pairwise independence and the Chebyshev
inequality
4.1.1
Improvement to the proof of Shannons coding theorem, using linear codes
Very commonly, in Algorithms, we have a tradeoff between how much rand
Probability and Algorithms
Leonard J. Schulman
Problem set 6
Caltech CS150, Winter 2006
TA: Chih-Kai (Kevin) Ko.
Out Monday March 6. Due Wednesday March 15.
Week 8 reading: MU 11.1-11.2.
Exercises: MU 11.2, 11.3, 11.9, 11.14.
1
Probability and Algorithms
Leonard J. Schulman
Problem set 5
Caltech CS150, Winter 2006
TA: Chih-Kai (Kevin) Ko.
Out Wednesday February 22. Due Monday March 6.
Week 6 reading: MU 6.7-6.8, 7.1-7.4, proof of the Perron-Frobenius theorem in notes of Andries
Probability and Algorithms
Leonard J. Schulman
Problem set 4
Caltech CS150, Winter 2006
TA: Chih-Kai (Kevin) Ko.
Out Monday February 13. Due Monday February 20.
Week 5 reading: MU 6.1-6.6. Recommended also: the rst few chapters of Alon & Spencer (everythi
Ibid- Caltech Library System
Electronic Delivery Cover Sheet
WARNING CONCERNING COPYRIGHT RESTRICTIONS
The copyright law of the United States (Title 17, United
States Code) governs the making of photocopies or other
reproductions of copyrighted materials.
EE 150 Presentation
Week 6 L. Xiao, M. Johansson, H. Hindi, S. Boyd, A. Goldsmith: "Joint Optimization of Communication Rates and Linear Systems"
Ather Gattami, May 6, 2003
1
Problem Setup
w
LTI System
z
yr
Network
y
w: exogenous signal, including noises
Probability and Algorithms
Leonard J. Schulman
Problem set 1
Caltech CS150, Winter 2006
Out Friday January 6. Due Friday January 20.
Suggested references are listed on the course web page. Youre welcome to take advantage of other
references. However, real
Probability and Algorithms
Leonard J. Schulman
Problem set 2
Caltech CS150, Winter 2006
TA: Chih-Kai (Kevin) Ko.
Out Wednesday January 25. Due Friday February 3.
Week 3 reading: MU 1.3, 2. Exercises: MU 1.5, 1.7, 1.12, 1.14, 1.17, 1.21, 2.8, 2.12, 2.25, 3
Probability and Algorithms
Leonard J. Schulman
Problem set 3
Caltech CS150, Winter 2006
TA: Chih-Kai (Kevin) Ko.
Out Thursday February 2. Due Monday February 13.
Week 4 reading: MU 3.4, 4.5, 5.1-5.4.
Exercises: MU 3.20, 3.21, 3.24, 4.21, 4.22, 5.3, 5.10,
Ibid- Caltech Library System
Electronic Delivery Cover Sheet
WARNING CONCERNING COPYRIGHT RESTRICTIONS
The copyright law of the United States (Title 17, United
States Code) governs the making of photocopies or other
reproductions of copyrighted materials.