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3.
(30) Consider an undirected graph
G
=
(V, E),
where each undirected edge
{i,j}
has a corre
sponding cost
c{
i,
j},
which is an input to the minimum spanning tree problem.
Suppose that
V
{I, 2, .
.. ,20}. You have already computed a minimum spanning tree in the graph
G,
but
have lost part of the answer. You still know all of the edges with
both
endpoints among the nodes
{I, 2, .
.. , 10} (there are
k
of them). You also still know all of the edges with
both
endpoints among
the nodes {ll, 12,
... ,20} (there are
C
of them). What you have lost are all of the edges that have
one endpoint among the nodes {I, 2,
... , 1O} and one endpoint among the nodes {ll, 12,
... , 20} .
(a) (15) How many edges have you
los~~Hint:
how many edges are there in the minimum spanning
tree?)
A
ItA
S
T
"Uob
1i.:;'6'"
\::
1,01
~
(9
t.O'jt'!l. We. .,.",.,.
....
k
+1
eJ.j~
1.
C
We
need
tq~
....
J
r1&lrL
(b) (15) Suppose
that the following table gives a complete list of
all
of the edges in
G
with one
endpoint in {I, 2, .
.. ,10} and one endpoint in {ll, 12,
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 Fall '09
 TROTTER

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