Maybe I'm wrong, but your 2 farthest points should be on the boundary of
the maximum bounding circle (feels right but couldn't prove it).
Thus you would compute this circle, then filter points not too far from it,
then take the points with the max distance using an inner join (same as
Nick, but
Hallo
I haven't followed the whole conversation.
But one way is to collect alk points and usr ST_maxdistance on the colnections.
or st_longestline. longestline will return a line where the end points is the
two points furthest from eath other. Those functions is quite fast.
/Nicklas
Sent