Algorithms | Graph Shortest Paths | Question 8

In a weighted graph, assume that the shortest path from a source ‘s’ to a destination ‘t’ is correctly calculated using a shortest path algorithm. Is the following statement true?
If we increase weight of every edge by 1, the shortest path always remains same.
(A) Yes
(B) No


Answer: (B)

Explanation: See the following counterexample.

There are 4 edges s-a, a-b, b-t and s-t of wights 1, 1, 1 and 4 respectively. The shortest path from s to t is s-a, a-b, b-t. IF we increase weight of every edge by 1, the shortest path changes to s-t.


   1      1     1
s-----a-----b-----t
 \              /
   \          /
     \______/
        4


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