@@ -11,11 +11,13 @@ $x \in \mathbb{R}$ is a vector describing possible solutions. If $x \in \mathbb{

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@@ -11,11 +11,13 @@ $x \in \mathbb{R}$ is a vector describing possible solutions. If $x \in \mathbb{

Integer linear programms (ILPs) are linear programms with the additional restriction that all variables have to be integers: $x \in\mathbb{Z}$.

Integer linear programms (ILPs) are linear programms with the additional restriction that all variables have to be integers: $x \in\mathbb{Z}$.

The decision variant of an ILP is NP-complete.

The decision variant of an ILP is NP-complete.

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In this thesis we use a more readable notation which does not completely sticks to this definition. We write down the inequalities in a sum notation. (Maybe an example?) But it is possible to transform them into the matrix notation.

In this thesis we use a more readable notation which does not completely sticks to this definition. We write down the inequalities(and the objective function?) in a sum notation. (Maybe an example?) But it is possible to transform them into the matrix notation.

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Decision problems can be modelles with ILPs. Every variable $x_i \in\{0,1\}$ denotes a possible decision. In our case we assign a decision variable for each vertex to decide if it is included in a dominating set or not.

Decision problems(combinatorical optimisation problems?/ \textbf{Decisions}. Not Decision Problems) can be modelled with ILPs. Every variable $x_i \in\{0,1\}$ denotes a possible decision(To include or not?). In our case we assign a decision variable for each vertex to decide if it is included in a dominating set or not.

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(Maybe to "formal". Maybe introduce the used notation right away and try to find textbook or publication which also uses this notation to cite)