text: abstract
  this paper attacks the following problem. we are given a large number n of
  rectangles in the plane, each with horizontal and vertical sides, and also a number
  r < n . the given list of n rectangles may contain duplicates. the problem is
  to find r of these rectangles, such that, if they are discarded, then the intersection
  of the remaining (n − r) rectangles has an intersection with as large an area as
  possible. we will find an upper bound, depending only on n and r, and not on the
  particular data presented, for the number of steps needed to run the algorithm on
  (a mathematical model of) a computer. in fact our algorithm is able to determine,
  for each s ≤ r, s rectangles from the given list of n rectangles, such that the
  remaining (n − s) rectangles have as large an area as possible, and this takes
  hardly any more time than taking care only of the case s = r. our algorithm
  extends to d-rectangles—analogues of rectangles, but in dimension d instead of in
  dimension 2. our method is to exhaustively examine all possible intersections—this
  
  is much faster than it sounds, because we do not need to examine all ns subsets in
  order to find all possible intersection rectangles. for an extreme example, suppose
  the rectangles are nested, e.g., concentric squares of distinct sizes, then the only
  intersections examined are the smallest s + 1 rectangles.