  The classical and extensively-studied Fr\'echet distance between two curves
is defined as an inf max, where the infimum is over all traversals of the
curves, and the maximum is over all concurrent positions of the two agents. In
this article we investigate a "flipped" Fr\'echet measure defined by a sup min
-- the supremum is over all traversals of the curves, and the minimum is over
all concurrent positions of the two agents. This measure produces a notion of
"social distance" between two curves (or general domains), where agents
traverse curves while trying to stay as far apart as possible.
  We first study the flipped Fr\'echet measure between two polygonal curves in
one and two dimensions, providing conditional lower bounds and matching
algorithms. We then consider this measure on polygons, where it denotes the
minimum distance that two agents can maintain while restricted to travel in or
on the boundary of the same polygon. We investigate several variants of the
problem in this setting, for some of which we provide linear time algorithms.
Finally, we consider this measure on graphs.
  We draw connections between our proposed flipped Fr\'echet measure and
existing related work in computational geometry, hoping that our new measure
may spawn investigations akin to those performed for the Fr\'echet distance,
and into further interesting problems that arise.
