Idea: Instead of looking onto edges, look on two consecutive edges

[d-krupke]

If only looking onto a single edge, we may have to cut of a lot of its length. It also does not consider that we have to continue with another circle. Instead, we could look onto triples uvw and compute for all pairs the cheapest CE-TSP connection. This will at least at v not require us to cut of the circles radius. You can get a very simple lower bound by just summing up the cheapest such triple divided by two for every circle. You can also enforce more constraints on the connectivity and maybe even integrate it in one of the approximation algorithms.

Note that this boosts the size of the problem to n^3 (instead of n^2 when only considering edges). However, we should probably also with this idea just consider a subset of the circles.

[d-krupke]

Does not give use any good results. Only improves the lower bound at the top level, but does not allow much pruning.