Question 1 (Price Functions and Edge Modifications, 20 points). Let G be a stron

Question

Question 1 (Price Functions and Edge Modifications, 20 points). Let G be a strongly connected, directed graph with (possibly negative) edge weights and no negative weight cycles. Suppose that for some vertex s in G that we have already computed all of the shortest path lengths d(v) from s to each vertex v of G. Recall in class that we discussed that path lengths in G could be related to paths with the edge weights replaced biy ?'(u,v) -L(u, v) + d(u) - d(v) 2 0. Suppose that a single edge of G has its weight changed. Show that there is a nearly linear time algorithm to compute the single source shortest paths from s on this new graph.

Explanation / Answer

Solution:

The above algorithm is running for a very vertex in the DAG, which means the time complexity will be linear.

On the way to the checking of the path is changed the vertices length is also getting displayed to let you know if the newly added edge will affect the shortest distance to the vertices.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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