shortestPathsex - Engineering Exercises 1. The figure below...

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Engineering xercises Exercises 1. The figure below shows an intermediate state in the execution of the labeling algorithm for shortest paths starting at vertex a . The 2. Let G be a digraph in which edges have “capacities”. The bottleneck capacity of a path in G is the minimum edge capacity on heavy edges are the tree edges defined by parent pointers in the implementation. The distance values are shown next to the nodes in the diagram. the path. A best bottleneck path tree is a spanning tree of G in which each path has the largest possible bottleneck capacity. Let T be a spanning tree of G with root s and let bcap ( u ) be the bottleneck capacity of the path from s to u in T . Show that if T is a best bottleneck path tree, then bcap ( v ) min{ bcap ( u ), cap ( u , v )}, for ll d ( i 4 5 h j b 3 14 all edges ( u , v ) in G . If bcap ( v )<min{ bcap ( u ), cap ( u , v )} for some edge ( u,v ) then there is a path to v with a larger bottleneck capacity than the tree path, implying that T is not a best bottleneck path tree. Therefore, if T is a best bottleneck path
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shortestPathsex - Engineering Exercises 1. The figure below...

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