I have a list of thousands 3D vectors $(x_i, y_i, z_i)$. These are too many to work with so i want to reduce their number. For that cause, i implemented the following criterion:
If a $j$ exists such that:
- $x_j \le x_i$ and
- $y_j \le y_i$ and
- $|z_j| \ge |x_i|$
then vector $i$ gets eliminated from the list.
My question now is whether the number of vectors produced by the aforementioned elimination process is bounded or not.
If the number of vectors surving is $k$ and the original population $p$, is there an $n$ such that:
$p > n \ge k$ ?
PS: I wrote a program in python for this and managed to reduce the number of vectors significantly. I tried it in a lot of sets and indicatively i got from ~75000 to ~100. In some cases i got more than 200 though (216 to be exact) which seems a bit too many..