* Test the ASP version on the graphs from week 5 to compare them. (saturday) ✔

- The ASP version performs quite bad on many random graphs where the ILP version performs quite good. One key factor that I could determine is that on those random graphs were the ILP version was good the difference in the size of an unconnected solution and a connected is rather low. So the ILP version seems to handle those instances were there is no big difference good.

- The ASP version performed in general better on grid graphs. This is what I expected as the ASP version was better on the leaf graphs as well. My assumption still is that there are too many "alternative" unconnected solutions where it is much cheaper to replace nodes from an previous unconnected solution and to generate a new unconnected solution than to add those vertices which separate them. As for those instances where the ILP needs a lot of time to solve the number of lazily added constraints is very high and the gap decreases(my test results) very slow both of these facts seem to underline my assumption.

* Test the (new) implementation on the usual graphs and them from week 5. (saturday) (❌)

* Test the (new) implementation on the usual graphs and them from week 5. (saturday) (❌)

- Only tested on a few graphs as the testing costs much time. But the decrease in runtime was significant.

* Create clean tables and CSV files. (sunday) (❌)

* Create clean tables and CSV files. (sunday) (❌)

- As I tested many graphs I have to further select which graphs I really want to include and I might have to do new tests if I change the implementation.

## thesis

* Begin the paragraph of results. (wednesday) (✔)

- I wrote those bullet points that I want to include in a text file. But I haven't created an tex file yet.

* Refactor the paragraph for Implementation and methods. (wednesday) ✔

# Week 7

## thesis

* According to Elines feedback.

- Move definitions from methods to a preliminary section and move the intro into ILP's to this section. ✔

- Move the stuff from the implementation section to the methods section and mix it up a bit. (✔)

- (The implementation section was removed for now and its content was moved to methods. Most of the definitions from the preliminaries section should be moved to method section and mixed up with the content)

- Rework the part with the vertex separators and be more precise and specific. ✔

- Add missing stuff. (❌)

- Different type of constraints to enforce connectivity. (✔)

- I wrote a german draft to get an idea how to do it.

- Different constraints that I tried to strengthen the ILP formulation and preventively adding separator constraints. ❌

## python

### runtime

* Check how large is the difference between the size of a minimum dominanting set and a rooted connected minimum dominating set for all test instances.

- Done for leafs. ✔

# Week 8

## thesis

* Mix the stuff from the methods section and the definitions up a bit.

* Add missing stuff. (Highest priority! Rather have awfull stuff that can be refinded than having the feeling of getting stucked!)

- Different type of constraints to enforce connectivity.

- Different constraints that I tried to strengthen the ILP formulation and preventively adding separator constraints.

- Introduction

- Table of results

- Discussion

- Implementation

## python

### runtime

* Check how large is the difference between the size of a minimum dominanting set and a rooted connected minimum dominating set for all test instances.

- GNM 250 graphs.

- GNM 100 graphs.

## python

### runtime

* For the leaf instances, the grid graphs and some of the random graphs:

- measure the size of a minimal unconnected solution and how fast the added separators close the gap.