@@ -85,6 +85,7 @@ With PyCharm and Visual Studio Code, there are integrated plugins and you won't
> Every participant has to show individually that he/she has a working environment, as this is of fundamental importance. We will do this remotely via screen sharing, such that you can also use your desktop computer.
## Task 2: Take a look into the code of the examples
We implemented three examples, one for every technique, for you.
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@@ -110,8 +111,8 @@ The definition for these problems should be just some _variables_, a few rules,
As an example, let us take a look on the Minimum Spanning Tree problem.
We are given a graph $G=(V,E)$ with edge weight $w: E \rightarrow \mathbb{R}^+_0$.
Let us use the boolean variables $x_e, e \in E$ with $x_e=1$ if $e$ is in the MST, and $x_e=0$ otherwise.
As we are using the Minimum Spanning Tree, the objective is $$\min \sum_{e \in E} w(e)\cdot x_e$$.
The constraints are $$\sum{e \in E} x_e == |V|-1$$ to enforce exactly $|V|-1$ edges, and for every real and not-empty subset $V' \subsetneq V$, $$\sum_{uv\in E, u \in V', w \not\in V'} x_{uv} \geq 1$$ to make sure that every component is connected to the remaining graph.
As we are using the Minimum Spanning Tree, the objective is $$\min \sum_{e \in E} w(e)\cdot x_e$$
The constraints are $$\sum_{e \in E} x_e = |V|-1$$ to enforce exactly $|V|-1$ edges, and for every real and not-empty subset $V' \subsetneq V$, $$\sum_{uv\in E, u \in V', w \not\in V'} x_{uv} \geq 1$$ to make sure that every component is connected to the remaining graph.
We could actually skip the first constraint, as the objective will make sure we will not use more edges than necessary.
* We will ask you to give us a quick informal defintion of the problems (which can be an example) and then show us the mathematical definition (with a rough idea what it states).
