The Metropolis Regional Authority (MRA) is planning the construction of a light rail network connecting the major
Question:
The Metropolis Regional Authority (MRA)
is planning the construction of a light rail network connecting the major activity centers of the region.
The figure below shows the 9 centers involved along with possible segments connecting them.
Estimated costs of construction are also shown on each such link (in $ million).
Eventually traffic on the chosen background network will be organized into routes with intermediate stops. For now, however, MRA simply wants to find the least total cost background network that offers a path between each pair of the 9 centers.
(a) Explain why an optimal background network for the MRA light rail will be a minimum total weight spanning tree of the graph below.
(b) Apply Greedy Algorithm 10F to compute such a minimum weight spanning tree, commenting on how subtrees are formed and merged as the algorithm proceeds, and on why some attractive edges were skipped.
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