We show that the Hausdorff distance for two sets of non-intersecting line
segments can be computed in parallel in O(log2n) time using O(n)
processors in a CREW-PRAM computation model. We discuss how some parts of the
sequential algorithm can be performed in parallel using previously known
parallel algorithms; and identify the so-far unsolved part of the problem for
the parallel computation, which is the following: Given two sets of
x-monotone curve segments, red and blue, for each red segment find its
extremal intersection points with the blue set, i.e. points with the minimal
and maximal x-coordinate. Each segment set is assumed to be intersection
free. For this intersection problem we describe a parallel algorithm which
completes the Hausdorff distance computation within the stated time and
processor bounds