Linear Programming and Approximation Algorithms

10:00-11:15pm TTh, ECSS 2.203

in Room ECSS 3-611.

Office Hours: ???

Room: ??

email: [email protected]

Design and Analysis of Approximation Algorithms

Unpublished Lecture Notes (available in class)

Vjiay Vazirani:

Approximation Algorithms

Springer 2001

Chapter 1 Introduction (1) constant-Approximation

Chapter 1 Introduction (2) PTAS

Chapter 7 Linear Programming
(1) Simplex Method

Chapter 7 Linear Programming
(2) Combinatorial Rounding

Chapter 7 Linear Programming
(3) Pipage Rounding

Reading
for Pipage Rounding

Chapter 7 Linear Programming
(4) Ellipsoid Method

Reading
for Ellipsoid Method

Reading
for Ellipsoid Method

Reading
for Ellipsoid Method

Chapter 7 Linear Programming
(5) Iterative Rounding

Chapter 7 Linear Programming
(6) Random Rounding

Open Problems
Target Coverage

Chapter 8 Primal-Dual Method and Local
Ratio (1) Duality of LP

Chapter 8 Primal-Dual Method and Local
Ratio (2) Primal-Dual Approximation Schema

Chapter 8 Primal-Dual Method and Local
Ratio (3) Local Ratio

Chapter 8 Primal-Dual Method and Local
Ratio (4) Network Problem

Chapter 8 Primal-Dual Method and Local
Ratio (5) Equivalence

Problem Solving and Research Seminar

Reading
for Local Ratio

Reading
for Local Ratio

Reading
for Local Ratio

Chapter 9 Semi-definite Programming
(1) What is SDP?

Chapter 9 Semi-definite
Programming (2) Interior Point Method

Chapter 9 Semi-definite
Programming (3) Primal-Dual Interior-Point Method

Chapter 9 Semi-definite Programming
(4) Interior-Point Method for SDP?

Chapter 9 Semi-definite Programming
(5) Hyperplane Rounding

Chapter 9 Semi-definite Programming
(6) Outward Rotation

Chapter 9 Semi-definite Programming
(7) Multivariate Normal Rounding

Problem Solving and Research Seminar

Chapter 10 Inapproximatbility
(1) Many-One Reduction with Gap

Chapter 10 Inapproximatbility
(2) Gap Amplifying and Preserving

Chapter 10 Inapproximatbility
(3) L-reduction and APX-Complete

Chapter 10 Inapproximatbility
(4) PCP Theorems

Chapter 10 Inapproximatbility
(5) O(log n)-Inapproximability

Chapter 10 Inapproximatbility
(6) n^{O(1)}-Inapproximability

Chapter 10 Inapproximatbility
(7) Unique-Game-Hardness

Problem Solving and Research Seminar

a research seminar is designed to discusss possible

research project. Students are encourage to bring

their research project to the research seminar. Based

on contributions in the discussion, students will be organized

into groups to write papers. Grade will be given based on

the research performance of each student.

Please submit your report on Nov 30 about your idea on research problems that we discussed in classes.