The TAP problem and the CacAP problem can be seen as covering problems for the minimum cuts of a graph.
It seems like these problems would fall under the framework of network design problems (approximately) solvable with the primal-dual method.
However, I cannot find anything in the literature using these methods. Is a primal-dual approximation algorithm known for TAP or CacAP? Would it be interesting to find one, even if it does not improve upon the current best approximation ratios?