Consider an undirected graph G = (V,E) with positive weights we. Suppose that you have computed...

 

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Consider an undirected graph G = (V,E) with positive weights we. Suppose that you have computed a minimum spanning tree G, and that you have also computed shortest paths to all vertices from a particular vertex s E V. Now suppose each edge weight is increased by 1: the new weights are w' = we + 1. (a) (15 points) Does the minimum spanning tree change? Give an example where it changes or prove it can not change. (b) (15 points) Do the shortest paths change? Give an example where they change or prove they cannot change. Consider an undirected graph G = (V,E) with positive weights we. Suppose that you have computed a minimum spanning tree G, and that you have also computed shortest paths to all vertices from a particular vertex s E V. Now suppose each edge weight is increased by 1: the new weights are w' = we + 1. (a) (15 points) Does the minimum spanning tree change? Give an example where it changes or prove it can not change. (b) (15 points) Do the shortest paths change? Give an example where they change or prove they cannot change.