This preview shows page 1. Sign up to view the full content.
CSE 441T/541T Advanced Algorithms
Fall 2008
Homework 4a: More NPCompleteness, and Approximation
Assigned: October 29, 2008
Due Date: November 5, 2008
For NPcompletness reductions, unless otherwise indicated, you should reduce from
one of: SAT, 3SAT, SUBSETSUM, PARTITION, CLIQUE, INDEPENDENT SET,
or VERTEX COVER. You must submit your homework with a signed cover sheet
attached to the front.
Core Problem
1. (15 pts) In class, we showed that INDEPENDENTSET
≤
p
VERTEXCOVER. Recall that
a graph
G
with
n
vertices has an independent set of size at least
k
iﬀ it has a vertex cover of
size at most
n

k
; in particular, the vertices
not
in the cover form an independent set.
In class, we saw a 2approximation algorithm
A
for ﬁnding the minimal vertex cover. Pro
fessor Ptolemy suggests that one can derive a constantfactor approximation algorithm for
independent set by ﬁrst reducing it to a vertex cover problem as above, then applying algo
rithm
A
. Is the professor correct? Justify your answer, either by proving that there exists a
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/13/2009 for the course CSE 441 taught by Professor Cse441 during the Spring '08 term at Washington University in St. Louis.
 Spring '08
 cse441
 Algorithms

Click to edit the document details