Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 10, 2009
Lecture 1
Scribe: Jesse Geneson (2009)
Lecturer: Jonathan Kelner
1
Overview
The classs goals, requirements, and policies were introduced, and topics in the class were described. Every
thing in the overvie
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 20, 2009
Lecture 11
Lecturer: Jonathan Kelner
1
Scribe: Chaithanya Bandi
Outline
Today well introduce and discuss
Polar of a convex body.
Correspondence between norm functions and originsymmetric bodies (and see
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
10/8/2009
18.409 An Algorithmists Toolkit
Lecture 9
Lecturer: Jonathan Kelner
At the end of the previous lecture, we began to motivate a technique called Sparsication. In this lecture,
we describe sparsiers and their use, and give an overview of Combinato
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 22, 2009
Lecture 12
Scribes: Alex Levin (2009)
Lecturer: Jonathan Kelner
1
Outline
Today well go over some of the details from last class and make precise many details that were skipped. Well
then go on to prove Fri
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 30, 2009
Lecture 7
Lecturer: Jonathan Kelner
1
Scribe: Alan Deckelbaum (2009)
Administrivia
There were two administrative announcements made at the beginning of class today.
The rst problem set will be posted on
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 29, 2009
Lecture 6
Lecturer: Jonathan Kelner
Scribe: Anthony Kim(2009)
Topics
Diameters and their relationship to 2
Expanders
Buttery networks
1
Diameters and Eigenvalues
So far, every time weve dealt with eige
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
November 3rd , 2009
18.409 An Algorithmists Toolkit
Lecture 15
Lecturer: Jonathan Kelner
1
Scribe: Justin Thaler
Outline
In this lecture we will design a method to randomly sample from a convex body, and this method will be a
subroutine in approximately c
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
10/29/09
Lecture 14
Lecturer: Jonathan Kelner
1
Approximating the volume of a convex b o dy
Exactly computing the volume a convex body is known to be #Phard, so the fact that we can approximate
its volume in P is surprisin
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 15, 2007
Lecture 2
Scribe: Mergen Nachin 2009
Lecturer: Jonathan Kelner
1
Administrative Details
Signup online for scribing.
2
Review of Lecture 1
All of the following are covered in detail in the notes for Lectu
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 17, 2009
Lecture 3
Lecturer: Jonathan Kelner
1
Scribe: Andre Wibisono
Outline
Todays lecture covers three main parts:
CourantFischer formula and Rayleigh quotients
The connection of 2 to graph cutting
Cheegers
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 10, 2009
Lecture 1
Scribe: Jesse Geneson (2009)
Lecturer: Jonathan Kelner
1
Overview
The classs goals, requirements, and policies were introduced, and topics in the class were described. Every
thing in the overvie
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 15, 2007
Lecture 2
Scribe: Mergen Nachin 2009
Lecturer: Jonathan Kelner
1
Administrative Details
Signup online for scribing.
2
Review of Lecture 1
All of the following are covered in detail in the notes for Lectu
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 17, 2009
Lecture 3
Lecturer: Jonathan Kelner
1
Scribe: Andre Wibisono
Outline
Todays lecture covers three main parts:
CourantFischer formula and Rayleigh quotients
The connection of 2 to graph cutting
Cheegers
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 22, 2009
Lecture 4
Lecturer: Jonathan Kelner
1
Scribe: Dan Iancu (2009)
Random walks
Let G = (V, E ) be an undirected graph. Consider the random process that starts from some vertex v V (G),
and repeatedly moves t
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 24, 2009
Lecture 5
Lecturer: Jonathan Kelner
1
Scribe: Shaunak Kishore
Administrivia
Two additional resources on approximating the permanent
Jerrum and Sinclairs original paper on the algorithm
An excerpt from M
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 24, 2009
Lecture 5
Lecturer: Jonathan Kelner
1
Scribe: Shaunak Kishore
Administrivia
Two additional resources on approximating the permanent
Jerrum and Sinclairs original paper on the algorithm
An excerpt from M
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
10/15/2009
Lecture 10
Lecturer: Jonathan Kelner
In this lecture, we shall revisit the Spectral Sparsiers and see a slightly dierent proof from last time.
We will then begin a new topic: Convex Geometry.
1
Spectral Sparsicat
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 22, 2009
Lecture 4
Lecturer: Jonathan Kelner
1
Scribe: Dan Iancu (2009)
Random walks
Let G = (V, E ) be an undirected graph. Consider the random process that starts from some vertex v V (G),
and repeatedly moves t
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
October 6, 2009
18.409 An Algorithmists Toolkit
Lecture 8
Lecturer: Jonathan Kelner
1
Scribe: Alessandro Chiesa (2009)
Administrivia
You should probably know that
the rst problem set (due October 15) is posted on the class website, and
its hints are a
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 27, 2009
Lecture 13
Lecturer: Jonathan Kelner
1
Scribe: Jonathan Pines (2009)
Outline
Last time, we proved the BrunnMinkowski inequality for boxes. Today well go over the general version of
the BrunnMinkowski ineq