2
$\begingroup$

Given

  • weighted directed graph $G = (V,E,w)$, where $w : E \to \mathbb R^+$
  • source vertex $v \in V$
  • vertex subset $U \subset V$

how to find a shortest directed path from $v$ containing all vertices from $U$? Note that such path may contain vertices that are not in $U$.

  1. Does such problem have a name?
  2. How to find a solution?
| cite | improve this question | |
$\endgroup$
2
$\begingroup$

This problem is NP-complete, by reduction from Hamiltonian path. Given an instance $G=(V,E)$ of Hamiltonian path, add a new vertex $s$ connected to all original vertices; this edges are directed from $s$, and all the original graph edges are bidirectional. Give all edges unit weight. There is a path from $s$ visiting all of $V$ of weight $|V|$ if and only if $G$ has a Hamiltonian path.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ The question asks not for complexity of the problem, but for known names. $\endgroup$ – Raphael♦ Apr 14 '14 at 18:16
  • $\begingroup$ @Raphael I'm actually interested both in an algorithm and in the name. I made it more clear in the question. $\endgroup$ – Jakub Stejskal Apr 14 '14 at 18:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.