Consider the shortest path problem from every node to node 1 and Dijkstra's algorithm. a) Assume that a positive lower bound is known for all arc lengths. Show how to modify the algorithm to allow more than one node to enter the set of permanently labeled nodes at each iteration. b) Suppose that we have already calculated the shortest path from every node to node 1, and assume that a single are length increases. Modify Dijkstra's algorithm to recalculate as efficiently as you can the shortest paths

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