CS601: HW 6 Solutions
October 6, 2009
1 (a)
KT11.1
Give an example where the greedy algorithm does not use the minimum
possible weights.
Sol. Weights: 4,3,2,1
K
= 5. Optimal is 2 but greedy uses 3 trucks.
1 (b)
Show that greedy algorithm is at most twice as worse as the optimal
Sol. Any consecutive trucks (
T
i
, T
i
+1
) must together have a load strictly greater than
K
, otherwise
T
i
+1
’s load could have been put in
T
i
itself. Suppose the algorithm returns
l
trucks as the answer.
We know that the total load is strictly greater than 0
.
5
*
l
*
K
. Hence atleast
d
0
.
5
l
e
trucks must
have been used in the optimal solution.
2
KT11.2
Give an algorithm that approximates the minimum representative set to
within a factor of
O
(log
n
)
.
Sol. We transform this problem to
Set Cover
as follows:
•
The elements of the universal set corresponds to different proteins.
•
For each protein
i
create a subset
S
i
that contains all proteins which are within a distance of
Δ from
i
.
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 Summer '09
 PROF.RANADE
 Algorithms, Set Theory, Optimization, Greedy algorithm, wi xi xi

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