  An encoder observes a point pattern---a finite number of points in the
interval $[0,T]$---which is to be described to a reconstructor using bits.
Based on these bits, the reconstructor wishes to select a subset of $[0,T]$
that contains all the points in the pattern. It is shown that, if the point
pattern is produced by a homogeneous Poisson process of intensity $\lambda$,
and if the reconstructor is restricted to select a subset of average Lebesgue
measure not exceeding $DT$, then, as $T$ tends to infinity, the minimum number
of bits per second needed by the encoder is $-\lambda\log D$. It is also shown
that, as $T$ tends to infinity, any point pattern on $[0,T]$ containing no more
than $\lambda T$ points can be successfully described using $-\lambda \log D$
bits per second in this sense. Finally, a Wyner-Ziv version of this problem is
considered where some of the points in the pattern are known to the
reconstructor.
