Pratition rectangle into smaller ones containig exactly 1 point, maximize wastelands area

Question

Given a rectangle R containing P points, orthogonal with axes, points are natural numbers.

Parcel is a rectangle which:

• is totally inside

Answer 1

I can think of a backtracking and exponentially hard method for starters. You pick your points in some order and each time do either of the following:

1- Decide to pass a vertical line 2- Decide to pass a horizontal line 3- Decide to ignore

Until you end-up with 3^n different cases.

For your own application, you could think of applying some bounding conditions at each iteration, e.g., verify if you have ended up with a parcel with no point inside, then backtrack.