Even faster point set pattern matching in 3D

Several recent papers have produced successively faster running times for solution of the Point Set Matching Problem (PSPM) (finding all congruent copies of a pattern in a sample set) in Euclidean 3-space, R3. Here, we obtain further improvement in the speed with which this problem can be solved. The source of the improvement over the previous fastest running time is a better upper bound for the volume of output, derived from a recent result. The previous best sequential running time for PSPM in R3 is O{kn2[(lambda) 6(n)/n$RT0.5 log n }, where k is the size of the pattern and n is the size of the sample set. Here, we give a sequential algorithm for the PSPM in R3 running in O[n2log n + kn1.8 log n (log*n)O(1)$RT time. Solutions to related problems are also discussed.