- This paper references several other papers which deal with the topic. So I've also read the following _An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets_. But they also used the vertex-separator constraints and a lazy approach.
- Their results quite good. So I guess it also makes sense to make some research how the graphs they used "looked like" and what characteristics they had that our graphs not have.
# Week 3
## Python
### runtime
* I found a bug in my implementation where vertex separators between connected subsets and the root where added
- I added some of the separators redundantly instead of adding different separators
- So I tried to fix this bug. If too many different separators are added beforehand the runtime increases again.
- And for whatever reason it seems like adding separators redundantly improves the runtime. I tried a different method where from the same set of separators, those separators where either added redundantly or separately. In the case where they were added redundantly the runtime was significantly better.
## thesis
* I wrote two paragraphs.
- The first about the methods and definitions used in the thesis.
- The second about the ILP-Models used and the implementation.
## literature
* I read through _Solving the Maximum-Weight Connected Subgraph Problem to Optimality_ to understand the connectivity constraints used here.
