  Consider a set P of points in the unit square U, one of them being the
origin. For each point p in P you may draw a rectangle in U with its lower-left
corner in p. What is the maximum area such rectangles can cover without
overlapping each other? Freedman [1969] posed this problem in 1969, asking
whether one can always cover at least 50% of U. Over 40 years later, Dumitrescu
and T\'oth [2011] achieved the first constant coverage of 9.1%; since then, no
significant progress was made. While 9.1% might seem low, the authors could not
find any instance where their algorithm covers less than 50%, nourishing the
hope to eventually prove a 50% bound. While we indeed significantly raise the
algorithm's coverage to 39%, we extinguish the hope of reaching 50% by giving
points for which the coverage is below 43.3%. Our analysis studies the
algorithm's average and worst-case density of so-called tiles, which represent
the area where a given point can freely choose its maximum-area rectangle. Our
approachis comparatively general and may potentially help in analyzing related
algorithms.
