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

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?

Create an algorithm for the Dijkstra Shortest Weighted Path based on the provided data.G is a weighted (directed or undirected) network, and s is a node in it.post-cond: specifies the shortest weighted route from s to each node of G, and d the lengths of those paths.

Subject: Information Security

If a Dijkstra's Algorithm only provides one shortest path from some starting node to some target node, provide an explanation on how we may change the algorithm so that it returns all shortest paths.