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In Simplifying a shapefile for world timezones

all generalize/simplify algorithms fail on 5 countries/states, shown in this shape file

The failure of the simplifying scripts is due to small rings below the size of the tolerance used for simplifying. The entire multi-polygon is deleted for each of these countries

How can I find and delete rings below a certain size with QGIS?

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First you have to explode the features in you shapefile, so that you don't have multi-polygones anymore (Multi-to-Single), then you add a column for the area and calculate the size for each polygon. Delete those which are smaller than the required size.

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