Pairwise Independence and Derandomization
Michael Luby & Avi Wigderson
Foundations and Trends in Theoretical Computer Science 2005
Michael Luby & Avi Wigderson
Pairwise Independence and Derandomization
Table of contents
Introduction to Pairwise Independen
arXiv:1008.1687v1 [cs.DS] 10 Aug 2010
A Deterministic Polynomial-time Approximation
Scheme for Counting Knapsack Solutions
Daniel Stefankovic
Santosh Vempala
Eric Vigoda
August 11, 2010
Abstract
Given n elements with nonnegative integer weights w1 , . . .
Two Lectures on the Ellipsoid Method for Solving
Linear Programs
1
Lecture 1: A polynomial-time algorithm for
LP
Consider the general linear programming problem:
= max cx
S.T.
Ax b, x Rn ,
(1)
where A = (aij )i,j Zmn is an m n integer matrix, and b = (bi
CS 7250, Approximation Algorithms
Midterm 1
Tue, March 1, 2011
Due NOON, Fri, March 4, 2011
Problem 1
Maximum directed cut is the following problem: Given a directed graph G(V, E ) with non-negative
edge costs, nd a subset S V so as to maximize the total
Where Can We Draw The Line?
On the Hardness of
Satisfiability Problems
Complexity
D.Moshkovits
1
Introduction
Objectives:
To show variants of SAT and check if
they are NP-hard
Overview:
Known results
2SAT
Max2SAT
Complexity
D.Moshkovits
2
What Do We
SIAM J. COMPUT.
Vol. 28, No. 2, pp. 525540
c 1998 Society for Industrial and Applied Mathematics
PRIMAL-DUAL RNC APPROXIMATION ALGORITHMS FOR SET
COVER AND COVERING INTEGER PROGRAMS
SRIDHAR RAJAGOPALAN AND VIJAY V. VAZIRANI
Abstract. We build on the class
M cnte-earlo AlgOrithIIlS for Enumeration and
Reliability Problems
Richard M. Karpt
University oJ California at Berkeley
Michael Lubyt
University
01 Toronto
In a similar spirit, we can discuss randomized approximation methods in which ~ and
0, as'well as
CS 7250, Approximation Algorithms
Homework 4
Thu, April 5, 2011
Due Tue, April 12, 2011
Problem 1
The performance guarantee OPT, > 0.878, for approximating MAXCUT was assuming that
the vector program (26.2) on page 256 of Vaziranis book can be solved opti
Constructive Algorithms for Discrepancy Minimization
Nikhil Bansal
arXiv:1002.2259v4 [cs.DS] 9 Aug 2010
Abstract
Given a set system (V, S ), V = cfw_1, . . . , n and S = cfw_S1 , . . . , Sm , the minimum discrepancy
problem is to nd a 2-coloring X : V cf
Rough Notes on Bansals Algorithm
Joel Spencer
A quarter century ago I proved that given any S1 , . . . , Sn cfw_1, . . . , n
there was a coloring : cfw_1, . . . , n cfw_1, +1 so that disc(Sj ) 6 n for
all 1 j n where we dene
(i)
(S ) =
(1)
iS
and disc(S )
The Ellipsoid Algorithm for Linear Programming
Lecturer: Sanjeev Arora, COS 521, Fall 2005 Princeton University
Scribe Notes: Siddhartha Brahma
The Ellipsoid algorithm for linear programming is a specific application of the ellipsoid method developed by S
CS 7250, Approximation Algorithms
Homework 1
Thu, Jan 20, 2011
Due Thu, Jan 27, 2011
Problem 1: Maxcut, Greedy Approximation Algorithm
Consider the cardinality maxcut problem, as dened in Vazirani Exercise 2.1 (page 22), and the
greedy algorithm given als
CS 7250, Approximation Algorithms
Homework 2
Tue, Feb 1, 2011
Due Tue, Feb 8, 2011
Problem 1: Greedy Vertex Cover
Perhaps the rst strategy one tries when designing an algorithm for an optimization problem is the
greedy strategy. For the unweighted vertex
CS 7250, Approximation Algorithms
Homework 3
Thu, Feb 17, 2011
Due Thu, Feb 24, 2011
Problem 1: Primal-Dual, Exact Complementary Slackness
This exercise is a review of the basics of LP-duality (chaper 12 in Vaziranis book).
(a) Let G(V, E ) be an undirect