Before revision:  The more general problem of covering a set of N segments (not necessarily disjoint) by min-area disjoint  polygons can also be solved in near linear time   .
After revision:  The more general problem of covering a set of N segments (not necessarily disjoint) by min-area disjoint polygons can also be solved in near linear time . A similar result is already known, see the work by Barba et al. .