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Unformatted text preview: true or false. 4. Suppose that e is a minimum weight edge G , and all the edge weights are distinct. Then e is always contained in the minimum spanning tree of G . True. Kruskals algorithm will start with this edge. 5. The path between a pair of vertices in a minimum spanning tree for G must be a shortest (i.e., least-cost) path between the two vertices in G . False. Note the difference between Prims algorithm and Dijkstras algorithm. You can create a counter-example. 6. Suppose we run Dijsktra's algorithm on G starting at some vertex, s . Recall that at each step of the algorithm, we add another vertex to the set S . Suppose we add vertex u to S before we add the vertex v to S . Then the distance from s to u in G is no greater than the distance from s to v . True. Note the proof of Dijkstras algorithm....
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- Spring '12