 
Summary: Pattern Matching for Spatial Point Sets \Lambda
David E. Cardoze
Leonard J. Schulman
College of Computing
Georgia Institute of Technology
Atlanta GA 303320280
fcardoze, schulmang@cc.gatech.edu
Abstract
Two sets of points in ddimensional space are given: a
data set D consisting of N points, and a pattern set or probe
P consisting of k points. We address the problem of deter
mining whether there is a transformation, among a specified
group of transformations of the space, carrying P into or
near (meaning at a small directed Hausdorff distance of) D.
The groups we consider are translations and rigid motions.
Runtimes of approximately O(n log n) and O(n d log n) re
spectively are obtained (letting n = maxfN; kg and omit
ting the effects of several secondary parameters). For trans
lations, a runtime of approximately O(n(ak + 1) log 2 n) is
obtained for the case that a constant fraction a ! 1 of the
