- May implement My Ky's, even if it is not optimal/ 100% correct. Just to observe if there is a connection between symmetrical unconnected solutions and the runtime and how strong this connection is. (Possible indicators: runtime, number of lazily added constraints) ❌

- Unfortunately her symmetry breaker made use of edges and our model consists only of node variables.

- Until now there has no symmetry breaker come to my mind and I haven't recognised one in a paper yet.

### runtime

* Create random graphs and try to compare runtime between ILP and ASP.

- Measure some characteristics of the graphs such as density, |V|, |E|, maximum degree, minimum degree, average degree, (maybe standard derivation of degree or median degree?)

- Measure some characteristics of the graphs such as density, |V|, |E|, maximum degree, minimum degree, average degree, (maybe standard derivation of degree or median degree?) ✔

- The graphs have been tested on random graphs with different size (|V| = 10, 20, 50, 100, 250, 500) with each size having 10 density(0.1, 0.2, ..., 0.9) levels.

- The results of this implementation were comparable to the one from _An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets*_.

- On random graphs the implementation can handle much more vertices than on our graphs.

- A fact that is *very* interesting is that on gridlike graphs the implementation performs way worse. Even when those graphs have similar density and much less vertices.

- A major problem seems to be a low average degree and a low maximum degree of the nodes!

- It seems to be as I assumed that when "high value" vertices are missing there are to many alternatives which have to be excluded in the iteration process.

- I should create tables with the differences in characteristics of those gridlike graphs and random graphs.

- On "thin" random graphs (width << length) the algorithm performs much better as there are not so many alterantive I assume.

- Measure and note gap between |D| of a minimal connected and a minimal unconnected solution. Measure for each |D| number of unconnected solutions which were found(ILP-only) and how many constraints where added in sum.

- Measure the time which was needed to find the first (nearly) optimal solution (strong upper bound) and the time needed to close the gap.

* Make some more detailed tests and check for the following connections: