This is a follow up to a problem I posted here: Modelling a data-sensitivity scenario as an ILP problem
As a recap, I was interested in finding the minimum number of cells that need to be suppressed to hide the values of certain cells. Now I'm also interested in finding upper and lower bounds for each cell. Take the following array:
\begin{array}{|c|c|c|c|c|c|} \hline & & & & & \text{Total}\\ \hline & X & X & 56 & 12 & 155\\ \hline & 32 & 93 & X & 37 & X\\ \hline & 54 & 75 & 12 & 13 & 154\\ \hline & 75 & X & 21 & 88 & X\\ \hline & 37& 26&X & 51 & X\\ \hline \text{Total} & X & X & 210 & 201 & 952 \\ \hline \end{array}
At this point, I'm no longer interested in suppressing cells but rather recovering cells. I want to set up an ILP to determine upper and lower bounds for each of the unknown cells, marked as $X$.
Does anyone have any ideas as to how I can go about this? I've been using the ILP in the previous post as something to work off of.