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What is the running time of an unweighted shortest path algorithm whose augmenting path is the path with the least number of edges?

(a) O(|E|)

(b) O(|E||V|)

(c) O(|E|^2|V|)

(d) O(|E| log |V|)

I have been asked this question in unit test.

My doubt stems from Flow Networks in division Flow Networks of Data Structures & Algorithms II

1 Answer

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Best answer
Right option is (c) O(|E|^2|V|)

The best I can explain: Each augmenting step takes O(|E|) using an unweighted shortest path algorithm yielding a O(|E|2|V|) bound on the running time.

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