Asst. 10 Solution
Spring 2009
Problem 1.
In the network shown, link costs labeled
are the same in both directions.
a) Find the minimum cost spanning tree
for broadcasting.
b) Why is the broadcast cost the same for any of the sources?
Would it always be the same if
costs were different in two different line directions?
c) Find the source tree for minimum cost from node A to each of
the other destinations.
d) Compare the total cost of broadcasting with the source tree with the total cost in a).
Solution.
a)
b) No matter which node is the source, the total cost is the sum of the costs on the 4 links
shown, since exactly one copy of a packet travels on each link. If the costs were different in
the two directions the broadcast costs and minimum spanning trees could be different. For
example if the link cost of 4 from A in the diagram were large or infinite in the opposite
direction to A, there would be a different broadcast minimum spanning tree from nodes
other than A.
c)
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 Spring '09
 JOHNMETZNER

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