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# 25 - also globally optimal We will discuss two algorithms...

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1 A minimum spanning tree of a weighted graph is a spanning tree whose sum of weights on edges is smallest possible among all spanning trees of the graph. A graph can have more than one minimum spanning tree, however we will show that if all weights on edges of the graph are different, then the minimum spanning tree is unique. In Figure 13.5 a minimum spanning tree is depicted in bold edges. There are efficient algorithms for constructing minimum spanning tree in a given graph. In fact there are greedy algorithms, so at each step the local best choice turns out to be

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Unformatted text preview: also globally optimal. We will discuss two algorithms here - one of Kruskal and Prim. 2 Apply Kruskal’s Algorithm to the graph. 3 4 Part 1) can be implemented using merge sort in Part 2) can be implemented using a technique of flag component by having a flag for each edge reporting the corresponding component it belongs to in 5 Apply Prim’s Algorithm to the graph. 6 Show that if the weight of each edge in a graph is unique then the graph has unique minimum spanning tree....
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25 - also globally optimal We will discuss two algorithms...

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