CS 473G: Combinatorial Algorithms, Fall 2005
Homework 3
Due Tuesday, October 18, 2005, at midnight
Name:
Net ID:
Alias:
Name:
Net ID:
Alias:
Name:
Net ID:
Alias:
Starting with Homework 1, homeworks may be done in teams of up to three people. Each team
turns in just one solution, and every member of a team gets the same grade.
Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above.
Staple this sheet to the top of your homework.
1. Consider the following greedy approximation algorithm to ﬁnd a vertex cover in a graph:
GreedyVertexCover
(
G
):
C
←
∅
while
G
has at least one edge
v
←
vertex in
G
with maximum degree
G
←
G
\
v
C
←
C
∪
v
return
C
In class we proved that the approximation ratio of this algorithm is
O
(log
n
); your task is to
prove a matching lower bound. Speciﬁcally, prove that for any integer
n
, there is a graph
G
with
n
vertices such that
GreedyVertexCover
(
G
) returns a vertex cover that is Ω(log
n
)
times larger than optimal.
2. Prove that for
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 Fall '08
 Chekuri,C
 Algorithms, Graph Theory, Bipartite graph, Graph coloring, Approximation algorithm, Bin packing problem

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