well im new here
im not sure i fully understand the goal
but since this has been here for some time
you said any idea's

Basically, I have a two-dimensional array of boolean values representing an area of cells
My aim is to find an algorithm, which finds the minimum amount of rectangles within the green areas and their coordinates.
this sounds fascinatingly similar to something one might use with
a path-finding algorithm such as
dijkstra's or A star or some other variant

the basic premise might be modified to your needs
treating each grid section as a node
instead of using it as a search for a path
you might use it as a search to tally up all valid nodes per region
much like a paint fill algorithm
http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
because the way dijkstras works your basically turning everything into nodes
if you were to have one version treat green nodes as impassable and the other red
then simply perfoming a search at each unique area
would build up a list of nodes for a passable area
ie each region as if it were its own section
the length of which could be traverse and operated on
the length itself would be the amount of bools per area as stated above


i dunno if that helps
but it looks similar to a regular game algorithm problem for path or region finding

you will also see that these algorithms can be applied to vertices when treating them as nodes
there are videos and such that do it on you tube ect...