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     - 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. 
+
+
+