December 1, 1999
6.893 Approximability of Optimization Problems
Lecture 23
Lecturer: Madhu Sudan
1
Scribe: Anna Lysyanskaya
Introduction: custom-made PCPs
In this lecture, we will see how to tweak PCPs to make them yield hardness of approximation results.
6.893 Approximability of Optimization Problems
November 1, 1999
Lecture 14
Lecturer: Madhu Sudan
1
Scribe: Amit Sahai
Low Degree Testing
In this lecture, we introduce the notion of low degree testing. We have already studied multivariate
polynomial codes,
November 8, 1999
6.893 Approximability of Optimization Problems
Lecture 16
Lecturer: Madhu Sudan
Scribe: Yevgeniy Dodis
In this lecture will will complete the low-degree test (by talking about the bivariate polynomial test)
and start talking about PCPs ag
6.893 Approximability of Optimization Problems
October 27, 1999
Lecture 13
Lecturer: Madhu Sudan
1
Scribe: Ryan ODonnell
Linearity Testing Over f0, 1g With Fourier Analysis
In this lecture we look at an alternative view of linearity testing, introduced in
6.893 Approximability of Optimization Problems
November 15, 1999
Lecture 18
Lecturer: Madhu Sudan
Scribe: Adam Smith
In this lecture, we show that approximating polynomial constraint satisfiability (pcs) to within a constant factor is hard.
Recall the den
November 10, 1999
6.893 Approximability of Optimization Problems
Lecture 17
Lecturer: Madhu Sudan
1
Scribe: Venkatesan Guruswami
Overview of the Lecture
In this lecture we will rst design a PCP verier for NP languages that tosses polynomially many (in
fac
6.893 Approximability of Optimization Problems
December 6, 1999
Lecture 24
Lecturer: Madhu Sudan
Scribe: Prahladh Harsha
In todays lecture, we shall show that Set-Cover cannot be approximated to within a factor of
(1 ) log4 n for any > 0 unless NP DTIME(n
6.893 Approximability of Optimization Problems
November 29, 1999
Lecture 22
Lecturer: Madhu Sudan
1
Scribe: Matthew Frank
Hardness of Approximation
We will start with H
astads PCP and use it to generate a bound for approximations to the MAX-CUT
problem. I
6.893 Approximability of Optimization Problems
November 22, 1999
Lecture 20
Lecturer: Madhu Sudan
Scribe: John Dunagan
Introduction
In todays lecture, we will discuss the composition of proof systems and the proof of the main PCP
theorem. The theorem on t
November 24, 1999
6.893 Approximability of Optimization Problems
Lecture 21
Lecturer: Madhu Sudan
1
Scribe: Ryan ODonnell
Current versions of the PCP theorem; parallel repetition
and improved outer veriers; H
astads inner verier
1.1
Introduction
In the la
6.893 Approximability of Optimization Problems
October 25, 1999
Lecture 12
Lecturer: Madhu Sudan
Scribe: Sandeep Chatterjee
In this lecture, we consider self-testing alogrithms and in particular, a self-tester for Hadamard Codes.
We further discuss linear
6.893 Approximability of Optimization Problems
October 6, 1999
Lecture 9
Lecturer: Madhu Sudan
Scribe: Nati Srebro
PCP and Hardness of Aproximation
In this lecture, we will see how results about the existence of ecient PCP veriers can be used to
prove har
6.893 Approximability of Optimization Problems
September 22, 1999
Lecture 5
Lecturer: Michel Goemans
1
Scribe: Matthew Frank
The Primal-Dual Method
Lets look at an example weve seen before:
Minimum Weight Vertex Cover
Given:
G = (V, E ) and,
weights w1 ,
6.893 Approximability of Optimization Problems
September 15, 1999
Lecture 3
Lecturer: Madhu Sudan
1
Scribe: John Dunagan
Heavy Hammers for Approximation Algorithms
Today we will explore a powerful tool in the design and analysis of approximation algorithm
6.893 Approximability of Optimization Problems
September 13, 1999
Lecture 2
Lecturer: Madhu Sudan
Scribe: Alantha Newman
Today we will discuss and give examples of NP-hard optimization problems that can be reasonably
approximated in polynomial time by non
September 8, 1999
6.893 Approximability of Optimization Problems
Lecture 1
Lecturer: Madhu Sudan
1
Scribe: Rocco Servedio
Course Overview
This is a course about the approximability of optimization problems. The optimization problems which
we will consider
6.893 Approximability of Optimization Problems
September 20, 1999
Lecture 4
Lecturer: Madhu Sudan
Scribe: Adam Smith
4
A 3 -approximation algorithm for MAX-SAT
1
1
In the previous lecture we saw a 1 1 -approximation algorithm for max-sat based on rounding
September 29, 1999
6.893 Approximability of Optimization Problems
Lecture 7
Lecturer: Madhu Sudan
Scribe: Prahladh Harsha
In todays lecture, we shall wrap up our discussion on Multi-Cut, briey summarize the dierent
types of approximation algorithms we hav
6.893 Approximability of Optimization Problems
October 13, 1999
Lecture 10
Lecturer: Madhu Sudan
1
Scribe: Chandra Boyapati
Error Correcting Code (ECC)
To deal with the problem of the inevitable noise that occurs during information transmission (or storag
October 20, 1999
6.893 Approximability of Optimization Problems
Lecture 11
Lecturer: Madhu Sudan
Scribe: Anna Lysyanskaya
This lecture is on self-correction of polynomial codes.
1
Inroduction: Relevance to PCP
Suppose we want to prove is that a formula is
6.893 Approximability of Optimization Problems
October 4, 1999
Lecture 8
Lecturer: Madhu Sudan
Scribe: Leonid Reyzin
Hardness of Approximation
Types of Approximation Problems
In the exact optimization world, there are three common ways to look at problems
6.893 Approximability of Optimization Problems
September 27, 1999
Lecture 6
Lecturer: Madhu Sudan
Scribe: Eric Lehman
This lecture describes the set cover problem and introduces the multicut problem, which is discussed
further in the next lecture.
1
The S