& UD            in P [@NII]                       in P [@NII]                                                         
  UC & GD            $O(\ln d(V))$ [@SMF]              $O(\ln d(V))$ [@SMF]              $O(\ln d(V))$ [@Fuk]              $O(\ln d(V))$ [@Fuk]
                     $O(k)$ [@Ishii]                                                                                       
  UC & UD            in P [@NII]                       in P [@NII]                                                         

  :  Previous approximation ratios and hardness of approximation thresholds for [SL]{} problems. GC and UC stand for general and uniform costs, GD and UD stand for general and uniform demands, respectively.

Some additional results are as follows. Ishii, Fujita, and Nagamochi [@IFN2; @IFN] showed that undirected [SSL]{} with $\hat{\kappa}$ can be solved in polynomial time for $k \leq 3$, but is NP-hard if there exists a vertex $v \in V$ with $d(v) \geq 4$. Barasz, Becker, and Frank [@BBF] gave a strongly polynomial time algorithm for edge-connectivity directed [SSL]{} with uniform demands. Several generalizations of source location problems can be found in [@SMNF; @IM; @MUMF; @III].

Our results
-----------

Our first result is an easy consequence from Observation \[o:reduction\], and it illustrates the usefulness of the relation between the two problems.

\[t:hard\] Directed [SSL]{} for $k=1$ and unit costs is $\Omega(\log n)$-hard to approximate. Directed/undirected [$\kappa'$-SSL]{} with uniform demands can be solved in polynomial time.

Observations \[o:aug\] and \[o:reduction\] motivate the study of the [$a$-Based SNA]{} 