Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
Homework 4
Due: Thursday, March 20
1. Online Set Cover. In the online (unweighted) set cover problem, you are given a set system (U, S)
in advance with n elements and m sets. You just dont know wh
Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
Homework 2
Due: Tuesday, February 12
1. Approximation Algorithms for weighted Min-Vertex-Cover. For each of the following approximation algorithms for Min-Vertex-Cover with positive vertex weights
Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
H OMEWORK 6
Due: Thursday, May 1
Denitions: Given boolean functions f1 , . . . , fd , a k-query test is a probability distribution Pr on checks of the
form
(fi1 (x(1) ), . . . , fik (x(k) ).
Here
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 1: Denitions; greedy algorithm for Set-Cover & Max-Coverage
Jan 15, 2008
Lecturer: Ryan ODonnell
1
Scribe: Dafna Shahaf
Optimization Problems
An optimization problem is the problem of nd
Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
H OMEWORK 5
Due: Tuesday, April 1
1. Fourier expansion uniqueness. Using only Parsevals Theorem (and arithmetic) show that each f : cfw_1, 1n
R is uniquely expressible as a multilinear polynomial
Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
Homework 3
Due: Thursday, February 28
1. Some Generalizations of k-Center. These problems are not necessarily related to each
other so please dont read anything into their relative placement.
a) S
Advanced Approximation Algorithms
CMU 15-854B, Spring 2008
Homework 1
Due: Tuesday, January 29
1. Randomized approximation algorithms. Suppose A is a randomized algorithm for the
NP optimization problem Max-Blah and has the following properties:
i The exp
Advanced Approximation Algorithms
(CMU 15-854B, Spring 2008)
Lecture 5: Primal-Dual Algorithms and Facility Location
Jan 29, 2008
Lecturer: Anupam Gupta
Scribe: Varun Gupta
In the last lecture, we saw an LP rounding algorithm for the metric uncapacitated
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 2: LP Relaxations, Randomized Rounding
Jan 17, 2008
Lecturer: Ryan ODonnell
1
Scribe: Ali Kemal Sinop
Introduction
In the last lecture, a greedy log n -factor approximation algorithm was
Advanced Approximation Algorithms
(CMU 15-854B, Spring 2008)
Lecture 9: Hardness of Max-Ek-Indep.-Set and A.-k-Center
February 12, 2008
Lecturer: Ryan ODonnell, Anupam Gupta
Scribe: Eric Blais
In this lecture, we complete the proof of hardness of approxim
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 7: Asymmetric K-Center
February 5, 2007
Lecturer: Anupam Gupta
Scribe: Jeremiah Blocki
In this lecture, we will consider the K-center problem, both in its symmetric and asymmetric
varian
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 3: 1 vs 3/4 + Hardness for Max-Coverage
Jan 22, 2008
Lecturer: Ryan ODonnell
1
Scribe: Ravishankar Krishnaswamy
Outline
In this lecture, we prove that the 1 vs 3/4 + decision problem of
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 8: Hardness of Min-Ek-Hypergraph-Independent-Set
February 7 2008
Lecturer: Ryan ODonnell
1
Scribe: Aaron Roth
Introduction
In this lecture, we start to prove a hardness result for Max-Ek
Advanced Approximation Algorithms
(CMU 18-854B, Spring 2008)
Lecture 4: Uncapacitated Facility Location
Jan 24, 2008
Lecturer: Anupam Gupta
Scribe: S. Harsha Vardhan
In this lecture, as well as the next two lectures, we will study the uncapacitated facili