Step through Dijkstra's algorithm to calculate the single-source shortest paths from A to every other vertex. Show your steps by filling in the tables shown below. 14 12

Improve Luby’s MIS algorithm coded in Python by selecting a vertex at random,finding its neighbors and then finding the vertex with the minimum assignedrandom value to be included in the MIS.

Write pseudo-code to modify Dijkstra algorithm to find the shortest path with the least number of hops. Demonstrate your approach to find that shortest path from vertex 1 to vertex 7 in the following graph. Show your work. I 1 1 2 2 3 8 1 4 3 3 5 6 5 4 4 7

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