algorithm - Maximal rectangle set cover -


i've got binary matrix , i'm trying find largest rectangles can formed adjoining elements in matrix. largest rectangles mean, rectangles unique, non subsets of other rectangles. example, following matrix contains 6 such rectangles.

enter image description here

this related set cover problem, though here i'm interested in maximum number of rectangles, not minimum. approach i've tried find rectangles regardless of size, compare rectangles , remove them if subset of rectangle. not optimal approach. seems case of set cover problem shouldn't hard.

i've had , not found similar problem. there this paper, has ideas, still wide of mark. there name particular problem? there existing algorithms finding possible rectangles in set cover problem?

after bit more work, i've realised not related set cover problem. it's 'finding unique rectangles not contained within in other rectangle in binary matrix problem'.

i have come works well, have no idea it's complexity.

basically, line sweep across matrix horizontally , vertically. in each case, contiguous groups of 1's can form rectangles next line. results in number of rectangles, of duplicates or sub rectangles of others. these rectangles reduced unique set no rectangle sub rectangle of another. have rectangles.

here diagram relates image in original post:

enter image description here


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