The Minimum-(k,ρ)-Shortcut problem is NP-hard for k≥2 and ρ≥k+2 in directed and undirected graphs, while undirected graphs with ρ=k+1 are solvable in polynomial time.
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On the Complexity of the Minimum-($k,\rho$)-Shortcut Problem
The Minimum-(k,ρ)-Shortcut problem is NP-hard for k≥2 and ρ≥k+2 in directed and undirected graphs, while undirected graphs with ρ=k+1 are solvable in polynomial time.