Optimal way to cover a complete are making searching by zipcoe

I want to make a search by zip code, which is defined by polygons like in the picture below:

The thing is that actually, I can not make the search on the zip codes itself but in an area from the centroid of that zip code, for example for the zipcode 4, this area touch 1,2 and 5 as well.

In the same way, the search for 1 with takes the results from 2,3,4 and 6 as well.

Hence to avoid getting duplicates I want to take find out with are the zipcodes with which I can get all the results with the less number of searches, say take 4, and 6

Instead of 2,5 and 6

How can I approach this problem?

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