GATE | GATE CS 2020 | Question 50

Let G=(V,E) be a directed, weighted graph with weight function w:E→R. For some function f:V→R, for each edge (u,v)∈E, define w′(u,v) as w(u,v)+f(u)−f(v).

Which one of the options completes the following sentence so that it is TRUE ?

“The shortest paths in G under w are shortest paths under w′ too, _________”.
(A) for every f:V→R
(B) if and only if ∀u∈V, f(u) is positive
(C) if and only if ∀u∈V, f(u) is negative
(D) if and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G

Answer: (A)


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