The question is: Consider the directed graph with 5 vertices. Let the Dijkstra’s
algorithm yield shortest paths from node s to all the other nodes, as shown
in Fig. 1. Let the weight of the edge (x, t), increase and assume all nodes
somehow obtain this information. How does node s modify Dijkstra’s algorithm
to make minimum recomputations? Provide the final solution in the
form “Node s runs Dijkstra’s algorithm by initializing S as and maintaining the list (< each node >) as .”
My question is… Isn’t that a trick question because all it would do is increase the shortest path from s to t right?
alright so my picture isnt working
but it works something like this:
s->y->x->t
y also points to z.
y->z
these are one way directional arrows.
If (s,y), (y, z), (y, x), (x, t) are the only edges in this graph, then yes: this only increases the weight (or distance) of the shortest path of s to t, since there is only one such path.