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Asked: 2026-05-25T16:46:44+00:00

I’m designing an algorithm for finding the minimum distance of a given vertex v

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I’m designing an algorithm for finding the minimum distance of a given vertex v from a subset of vertices A(that is from an element of this subset).
I need to find the value k such that:

  • distance from x to v is k, for some x in A
  • distance from y to v is >=k, for all y in A.

My solution consist in:

  • getting the transpose graph G’
  • visiting G’ starting from v, using BFS.
  • find the minimum distance from the vertices in A

And I think this works and it should run in O(|V|+|E|) time.
My question is: there is a better solution to this problem?

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  1. Editorial Team

    No, there isn’t better solution.

    Consider the following: 1-2-3-4,A={4}, v=1. you will have to iterate all V,E in the graph [you must read all the path], making this problem Omega(V+E). since your algorithm is correct [simple to prove], and is O(V+E) [triviialy, creating G’ and BFS], and the problem is Omega(V+E), your solution is optimal, in terms of big O notation.

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