6.02 Practice Problems: Routing - MIT OpenCourseWare
No, they're not necessarily identical. Consider two paths between nodes A and B in graph G. One path takes 3 hops, each of cost 1, for a total cost of 3. The other path takes 1 hop, with a cost of 4. In this case, the shortest path between nodes A and B is the first one. Consider k=1 and h=1 and compute the costs and shortest paths in G'.
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