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abstract: |
    In [Source Location]{} ([SL]{}) problems the goal is to select a minimum cost source set $S$ such that the connectivity from $S$ to any node $v$ is at least the demand $d_v$ of $v$. In [Network Augmentation]{} ([NA]{}) problems we are given a graph $G=(V,E)$ and an edge-set $F$ on $V$, edge-costs on $F$ or node-costs on $V$, and connectivity requirements $\{r_{sv}:sv \in D\}$ on a set $D$ of “demand edges”. The goal is to compute a minimum cost edge-set $I \subseteq F$, such that in the graph $G+I$, the connectivity of each $sv \in D$ is at least $r_{sv}$. In [Rooted NA]{} $D$ is a star with center $s$, and in [$a$-Based NA]{} $F$ is a star with center $a$. We suggest a notion of $q$-connectivity, where every node $u$ has capacity $q_u \geq 1$ that represents the resistance of $u$ to failures. We observe that a large class of [SL]{} problems, including the variants that appear in the literature, is a particular case of $q$-connectivity [$s$-Based Rooted NA]{} problems. We use this to derive some approximation algorithms for [SL]{} from those for [NA]{}, as well as to derive some new results for [SL]{} problems. Some 