of our results are as follows.

    -   We observe that directed [SL]{} with unit costs is $\Omega(\log n)$-hard to approximate even with $0,1$ demands, while some versions of [SL]{} with uniform demands can be solved in polynomial time.

    -   We show that the $H(|D|)$-approximation algorithm of [@KN-aug] for edge costs [$a$-Based NA]{} has ratio $H(\alpha)$ for the $q$-connectivity version with node-costs, where $p_{\max}$ is the maximum number of parallel edges in $F$, $\alpha=\min\{r(D),|D| \cdot p_{\max}\}$, and $H(j)=\sum_{i=1}^j 1/i$ is the $j$th harmonic number. This gives a simple unifying $H(d(V))$-approximation algorithm for several [SL]{} variants considered separately by Sakashita, Makino, and Fujishige [@SMF]. Moreover, we will show that this is so whenever the connectivity function is submodular.

    -   For undirected [$a$-Based NA]{} we give an approximation algorithm with ratio $\min\{k,p_{\max} \ln k\} \cdot O(\ln k)$ for node-costs and $O(\ln^2 k)$ for edge-costs, where $k=\max_{v \in V}d_v$ is the maximum demand; the latter improves the ratio $\tilde{O}(k)$ of Fukunaga [@Fuk].

    -   We consider a variant of [SL]{} where we also have edge-costs and flow-cost bounds $\{b_v: v \in V\}$, and require that for every node $v$, the minimum cost of a flow of value $d_v$ from $S$ to $v$ is at most 