every bags, but only for priority bags. For non-priority bags we introduce $B_x$ and $B_x^s$ for all item sizes $s$ to hold all jobs from non-priority bags (with respective size $s$), giving us overall a smaller amount of possible patterns.

\[def:pat\] Let $p$ be a tuple with up to $q = \frac{1+2*\epsilon+\epsilon^2}{\epsilon^{k+1}} $ entries of the form $B_l^s$ with $s$ being any medium or large item size and $B_l$ either being a priority bag with $l\le b'$ or $B_l =B_x$ for indicating a slot for an arbitrary non-priority bag.

We call $p$ a valid pattern if and only if: $\sum\limits_{B_l^s \in p}{s} \le T = 1+2\epsilon+\epsilon^2$ and for every priority bag $B_l$ there is at most one entry of a size-restricted bag of $B_l$ in $p$. A valid pattern may hold an arbitrary amount of $B_x$ entries. Furthermore define $\mathscr{P}$ to be the set of all valid patterns.

One can imagine one entry $B_l^s$ of a pattern $p$ to be a slot reserved to the bag $B_l$ with size $s$. In case of an entry $B_x^s$ this slot will be reserved for a job of size $s$ of any non-priority bag. We want to remark that the relevant information of 