6.896 Topics in Algorithmic Game Theory
February 16, 2010
Lecture 4
Lecturer: Constantinos Daskalakis
Scribe: Jason Biddle, Alan Deckelbaum
NOTE: The content of these notes has not been formally reviewed by the
lecturer. It is recommended that they are re
6.896 Sublinear Time Algorithms
May 3, 2007
Lecture 24
Lecturer: Ronitt Rubinfeld Scribe: Ivaylo Riskov
1
Recap
f : cfw_0, 1n cfw_0, 1
x < y if i, xi yi f is monotone if x y, f (x) f (y ) We dene a violating edge (x, y ) such that y = x ei , x < y, f (x)
6.896 Sublinear Time Algorithms
April 26, 2007
Lecture 22
Lecturer: Ronitt Rubinfeld Scribe: Brendan Juba
1
Overview
We will continue examining sublinear time algorithms for clustering. Last time, we considered a set of n points and gave an algorithm to d
6.896 Sublinear Time Algorithms
April 24, 2007
Lecture 21
Lecturer: Ronitt Rubinfeld In this lecture, we are going to study property testing for clustering problems. Scribe: Ning Xie
1
Clustering problems
We will be working in d-dimensional Euclidean spac
6.896 Sublinear Time Algorithms
April 19, 2007
Lecture 20
Lecturer: Ronitt Rubinfeld Scribe: Erdong Chen
1
Graph Isomorphism =
We talked about a lower bound last time. Recall from last lecture (all are based on adjacent matrix model): Thm H known H unknow
6.896 Sublinear Time Algorithms
April 12, 2007
Lecture 18
Lecturer: Ronitt Rubinfeld Scribe: Ivaylo Riskov
1
Recap
c c log
c
Theorem 1 1-sided error testing for triangle-free property requires (
).
Theorem 2 Let P be any graph property in the adjacency ma
6.896 Sublinear Time Algorithms
April 10, 2007
Lecture 17
Lecturer: Ronitt Rubinfeld Scribe: Jacob Scott
1
Alons Theorem (adjacency matrix model)
Theorem 1 Let H be a xed graph with |H | = h, and PH be the property of not having H as a subgraph. Then, 1.
6.896 Sublinear Time Algorithms
April 5, 2007
Lecture 16
Lecturer: Ronitt Rubinfeld Recall from last lecture: Denition 1 The density between two disjoint non-empty sets A, B V is given by the formula d(A, B ) = e(A,B|) , where e(A, B ) is the number of ed
6.896 Sublinear Time Algorithms
April 3, 2007
Lecture 15
Lecturer: Kevin Matulef Scribe: Huy Le Nguyen
1
Denitions and Proof Plan
Lemma 1 (Szemeredis Regularity Lemma). For any , there exists C such that any graph G = (V, E ) can be partitioned into sets
6.896 Sublinear Time Algorithms
March 22, 2007
Lecture 14
Lecturer: Ronitt Rubinfeld Scribe: Huy Ngoc Nguyen
1
First order properties testing:
First order graph property is a property that can be expressed in the following form: R(u1 , ., uk , v1 , ., vl
6.896 Sublinear Time Algorithms
March 20, 2007
Lecture 13
Lecturer: Ronitt Rubinfeld Scribe: Huy Ngoc Nguyen
1
Bipartiteness testing on dense graph
Denition 1 G is f ar from bipartiteness if must remove at least n2 edges to make it bipartite. Denition 2 (
6.896 Sublinear Time Algorithms
March 15, 2007
Lecture 12
Lecturer: Ronitt Rubinfeld Scribe: Jeremy Hurwitz
1
1.1
Intro to Property Testers
Informal Overview
So far, weve dealt with two main types of approximations - multiplicative and additive. Such appr
6.896 Sublinear Time Algorithms
May 10, 2007
Lecture 26
Lecturer: Ronitt Rubinfeld Scribe: Chih-yu Chao
1
Recap from Last Time
1 2n xcfw_1n
Denition 1 (Fourier cocient) f (s) = f , s = Theorem 1 f,x f (x) = f (s)s (x)
f (x)s (x)
s[n]
Last time, we learne
6.896 Sublinear Time Algorithms
February 6, 2007
Lecture 1
Lecturer: Ronitt Rubinfeld Scribe: Chih-yu Chao
1
Testing Global Properties of Distributions
We will begin by considering how to test properties of distributions over large domains. We assume that
February 22, 2010
6.896 Topics in Algorithmic Game Theory
Lecture 6
Lecturer: Constantinos Daskalakis
Scribe: Jason Biddle, Debmalya Panigrahi
NOTE: The content of these notes has not been formally reviewed by the
lecturer. It is recommended that they are
6.896 Topics in Algorithmic Game Theory
Lecture 7
Lecturer: Constantinos Daskalakis
Scribes: David Chen, Pablo Azar
NOTE: The content of these notes has not been formally reviewed by the
lecturer. It is recommended that they are read critically.
Continuin
6.896 Topics in Algorithmic Game Theory
March 1, 2010
Lecture 8
Lecturer: Constantinos Daskalakis
Scribe: Alan Deckelbaum, Anthony Kim
NOTE: The content of these notes has not been formally reviewed by the
lecturer. It is recommended that they are read cr
6.896 Topics in Algorithmic Game Theory
February 17, 2010
Lecture 5
Lecturer: Constantinos Daskalakis
Scribe: Tony Liu
NOTE: The content of these notes has not been formally reviewed by the lecturer. It is recommended
that they are read critically.
We hav
6.005 Software Construction
Fall 2012
Profs. Adam Chlipala & Rob Miller
L14: Version Control
At this point, you might feel like Git is just an exotic torture that the 6.005
staff have devised to make it hard for you to know which version of your code
you
6.896 Topics in Algorithmic Game Theory
February 10, 2010
Lecture 3
Lecturer: Constantinos Daskalakis
Scribe: Pablo Azar, Anthony Kim
In the previous lecture we saw that there always exists a Nash equilibrium in two-player zero-sum
games. Moreover, the eq
6.005 Software Construction
Fall 2012
Profs. Rob Miller & Adam Chlipala
L16: Message Passing
Today
o
o
o
o
o
Client/server
Network sockets
Blocking
Wire protocols
Deadlocks
Required reading (from the Java Tutorial)
Make sure that you read and understand t
6.896 Topics in Algorithmic Game Theory
February 8, 2010
Lecture 2
Lecturer: Constantinos Daskalakis
Scribe: Yang Cai, Debmalya Panigrahi
In this lecture, we focus on two-player zero-sum games. Our goal is to show that linear programming
(LP) duality impl
6.005 Software Construction
Fall 2012
Profs. Rob Miller & Adam Chlipala
L15: Concurrency
Today
o
o
o
o
o
Message passing & shared memory
Processes & threads
Time slicing
Race conditions
Deadlocks
Required reading (from the Java Tutorial)
Make sure that yo
Approximation in
Algorithm Game Theory:
The Price of Anarchy
Tim Roughgarden
Stanford University
Pigou's Example
Example: one unit of traffic wants to go from
s to t
cost depends on congestion
c(x)=x
s
c(x)=1
t
no congestion effects
Question: what will se
6.896 Sublinear Time Algorithms
February 8, 2007
Lecture 2
Lecturer: Ronitt Rubinfeld Scribe: Adriana Lopez
In this lecture, we will prove a theorem from last lecture that states that there exists a closeness tester in L2 . We will also give an algorithm
6.896 Sublinear Time Algorithms
March 13, 2007
Lecture 11
Lecturer: Ronitt Rubinfeld Scribe: Christina Sauper
1
Estimating the Number of Connected Components
Given a graph G(V, E ) with max degree d and adjacency list representation and some , we want to
6.896 Sublinear Time Algorithms
March 8, 2007
Lecture 10
Lecturer: Ronitt Rubinfeld Scribe: Khanh Do Ba
1
1.1
Recap
Algorithm and notation
LZ77(w) 1 t1 2 repeat 3 nd longest substring wt .wt+ 4 if none then 5 next symbol = wt 6 tt+1 7 else 8 next symbol =