CS 573: Graduate Algorithms, Fall 2011
HW 1 (due Tuesday, September 13th)
This homework contains five problems.
Read the instructions for submitting homework on
the course webpage
. In particular,
make sure
that you write the solutions for the problems on
separate sheets of paper. Write your name and netid on each sheet.
Collaboration Policy:
For this home work students can work in groups of up to three students
each. Only one copy of the homework is to be submitted for each group. Make sure to list all the
names/netids clearly on each page.
Note on Proofs:
Details are important in proofs but so is conciseness. Striking a good balance
between them is a skill that is very useful to develop, especially at the graduate level.
1. (20 pts) Proofs are not necessary for the following two problems which should be easy reduc
tions from known problems.
•
(10 pts)
k
Bounded Set Cover
is the special case of
Set Cover
in which the car
dinality of each set is at most
k
. Describe a reduction to show that 3
Bounded Set
Cover
is NPHard.
•
(10 pts) A directed graph
G
= (
V, E
) is
strongly connected
if for all
u, v
∈
V
there
is a path in
G
from
u
to
v
and from
v
to
u
. The
StronglyConnected Spanning
Subgraph
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 Fall '08
 Chekuri,C
 Algorithms, Dynamic Programming, Computational complexity theory, Dominating set, NPcomplete, Subset sum problem, Partition problem

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