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Unformatted text preview: edges.
Run Dijkstra’s algorithm, times, once with each
vertex as source.
with more sophisticated data
structures. ¢ © ¢ ¦¤
§¥£ © ¡ ¨
© ¢ ¢ ¡ Solution 2: Assume no negative cycles.
Dynamic programming solution, based on a natural decomposition of the problem.
.
using “ repeated squaring”.
© ¦¤
¥£ ¢ ¢ ¡ © ¢ ¡ This lecture: Assume no negative cycles.
develop another dynamic programming algorithm, the
.
FloydWarshall algorithm, with time complexity
Also illustrates that there can be more than one way
of developing a dynamic programming algorithm.
© ¢ 3 ¢ ¡ Solution 3: the Input and Output Format
As in the previous dynamic programming algorithm,
we assume that the graph is represented by an
matrix with the weights of the edges: § © ¥ ¢
© ¥...
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 Spring '14

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