What is the name of the task or algorithm of identifying from a given set of those rectangles that are most unsuitable for tiling a given area?

Question

Mathematics

There is not enough horizons and terminology to google the solution or the closest answer.

Staging. There is an available 2D area at the input with properties {av_width, av_height} (available, in the sense) and a set of rectangles with properties {x, y, width, height}, which in an ideal world should tile the first available area. The problem is that a set of rectangles can be +-clumsy, that is, you need to:

1. Identify the most unsuitable polygons for tiling.
   
   It seems to be clear here: it is necessary to select those for which the proportion of intersection relative to their own area is maximum. On the other hand, it would be nice to not take into account intersections with 'excluded' rectangles, that is, in a naive attempt to solve each new exception will lead to a recalculation of the exceptions of the old ones. Some kind of relaxation is obtained, or whatever it is called.
   
2. Fit remaining rectangles until fully tiled (i.e. without 'gaps') of the available area.
   
   I don't even know how to get on.
   

Appendix. There is a window to which the user passes a string with a breakdown into regions (passes because the string can be shared and the session can be played back). Strictly speaking, in the elements of the breakdown list there is also the identifier of the resource opened in the subwindow (for example, let's say a file), but this does not apply to the task. The breakdown is not limited to a rectangular grid, for example, it can be as a column_of_thirds + a column_of_halves, and the same for rows. There is no grouping either, that is, the methods of tile managers seem to be inapplicable. Additionally , there is a restriction on the minimum height and width of the subwindow, but first I would like to find a solution without taking into account this restriction.

Thanks

Answer 1

Packaging tasks

Answer 2

First you need to clearly formulate the criterion for optimal tiling, in this case, those rectangles that were thrown out with such tiling will be the most inappropriate.