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Lecture CS174 17 Minimum Spanning Trees Remember the minimum spanning tree problem from CS170 you are given a graph G with weighted edges (real values on each edge) and the goal is to find a spanning tree T whose total weight is minimal. The minimum spanning tree is the least expensive way to connect up all the nodes. In the graph below, the minimum spanning tree is shown with heavy shaded edges. 5 12 17 10 8 4...
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Lecture CS174 17
Minimum Spanning Trees
Remember the minimum spanning tree problem from CS170 you are given a graph G with weighted edges (real values on each edge) and the goal is to find a spanning tree T whose total weight is minimal. The minimum spanning tree is the least expensive way to connect up all the nodes. In the graph below, the minimum spanning tree is shown with heavy shaded edges.
5 12 17 10 8 4 8
13
11
6
14
Minimum spanning trees are useful for designing networks: computer networks, communication networks, and distribution networks for utilities like electrical power, gas, water etc. The edges represent links between sites, and the edge weight is the cost of connecting those sites. The minimum spanning tree is the cheapest structure that connects all the sites. You usually want some redundancy (extra paths) in such a network but the min spanning tree is a good starting point for designing an inexpensive network.
De...
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