AFAIK there is no way to do this in a single pass.
One way to do it iteratively is:
- add a column which will flag features which are "nonoverlapping" (and which will be kept)
- choose one feature and flag it as nonoverlapping
- iterate {
   - delete all features which overlap some "nonoverlapping" feature
   - pick an unmarked feature and flag it as "nonoverlapping"
   - exit if all features are flagged as "nonoverlapping"
}

This is probably going to be slow...

Dylan Lorimer wrote:
Hey PostGIS Friends, here's a problem that's stumping me, hoping you can help:

I have a bunch of polygons, many of which overlap with each other. I
would like to trim down the set of polygons to only those that do not
overlap. I'm not particular about which I delete, so long as they
overlap by a certain %.

Any thoughts on how to do this? I was trying for a self join but can't
figure out how to not to delete all polygons that overlap.

Cheers,
dylan
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Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022

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