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courses:cs211:winter2011:journals:charles:chapter6 [2011/03/30 04:30] – [6.8 Shortest Paths in a Graph] gouldc | courses:cs211:winter2011:journals:charles:chapter6 [2011/03/30 04:49] – [6.8 Shortest Paths in a Graph] gouldc | ||
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We do this by incorporating divide-and-conquer principles into our algorithm. I'm slightly confused by the divide-and-conquer component to this problem. In class we did it with the graph in Figure 6.19. We started in the top left and found the shortest path to some midpoint, then we did the same thing from the bottom right. I will need to look in more depth at the pseudo-code on page 288 to get a better grasp of the concept. | We do this by incorporating divide-and-conquer principles into our algorithm. I'm slightly confused by the divide-and-conquer component to this problem. In class we did it with the graph in Figure 6.19. We started in the top left and found the shortest path to some midpoint, then we did the same thing from the bottom right. I will need to look in more depth at the pseudo-code on page 288 to get a better grasp of the concept. | ||
===== 6.8 Shortest Paths in a Graph ===== | ===== 6.8 Shortest Paths in a Graph ===== | ||
- | This section is about finding | + | Problem outline: We want to find the shortest path between two nodes in a directed graph. |
- | starting node s and destination node t with minimum total cost. Each edge in the graph has an associated weight. | + | Here we assume no negative cycles; otherwise a path could follow the negative cycle infinitely many times and so reduce the cost of the path to negative infinity. But that would be stupid. |
- | This section is about using a memoized array to keep track of the shortest paths in a graph. The new method is contrasted with Dijkstra' | + | |
+ | (6.23) //OPT(i,v) = min(OPT(i-1, |