Let's say I have the following area in a top-down map:

The circle is the player, the black square is an obstacle, and the grey polygons with red borders are walk-able areas that will be used as a navigation mesh for enemies. Obstacles and grey polygons are always convex.

The grey regions were defined using an algorithm when the world was generated at runtime.

Notice the little white column. I need to figure out where any empty space like this is, if at all, after the algorithm builds the grey regions, so that I can fill the space with another region.

Basically what I'm hoping for is an algorithm that can detect empty space next to a polygon.