Optimizing/complete coverage

[bahllr]

I am working on the following problem and now realizing that my previous (ridiculously complex solution), is only a partial solution. I would appreciate any help!

I have a matrix that can expand in either direction (limited to 220 rows and roughly 90 columns). I am indicating the intersections with '1' as below.

<table border="0" cellpadding="0" cellspacing="0" width="320"><col style="width: 48pt;" width="64" span="5"> <tbody><tr style="height: 15pt;" height="20"> <td class="xl69" style="height: 15pt; width: 48pt;" width="64" height="20">
</td> <td class="xl69" style="width: 48pt;" width="64">Area 1</td> <td class="xl69" style="width: 48pt;" width="64">Area 2</td> <td class="xl69" style="width: 48pt;" width="64">Area 3</td> <td class="xl69" style="width: 48pt;" width="64">Area 4</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 1</td> <td align="right">1</td> <td align="right">1</td> <td align="right">1</td> <td align="right">1</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 2</td> <td align="right">1</td> <td align="right">1</td> <td align="right">1</td> <td>
</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 3</td> <td>
</td> <td align="right">1</td> <td>
</td> <td>
</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 4</td> <td>
</td> <td align="right">1</td> <td>
</td> <td align="right">1</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 5</td> <td>
</td> <td>
</td> <td align="right">1</td> <td align="right">1</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 6</td> <td>
</td> <td>
</td> <td align="right">1</td> <td>
</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Topic 7</td> <td>
</td> <td>
</td> <td align="right">1</td> <td>
</td> </tr> </tbody></table>

I am looking for every combination of areas that will 'cover' or meet the topic requirements. So Topic 1 and 2 are 'covered' by area 1. But Topic 3 and 4 are covered by Area 2.....

So one 'solution' is: Topic 1,2 - Area 1
Topic 3,4 - Area 2
Topic 5,6,7 - Area 3

But there are multiple solutions and I am trying to outline them all....

I don't know if anyone has an idea about how this could be done. I am pretty familiar with VBA but not so much with matrix algebra or arrays....

I would really be keen on hearing peoples thoughts. Please let me know if I have not explained it well.

 

[bahllr]

In re-reading my post I realize that the output is somewhat unclear. i am looking to have each set of Areas arranged in columns like below:

Area 1 Area 2
Area 2 Area 4
Area 3

Each column represents a set of areas that have intersections ('1') that cover each topic.

Thanks.

 

[shg]

I think generating every combination of 90 areas is computationally intractable; that's 2^90 ~ 10^27 combinations to evaluate.