Faster point set pattern matching in 3-D

Abstract We improve upon the best previous upper bound for the volume of output for the Point Set Pattern Matching Problem (PSPM) in Euclidean 3-space, R 3 . This in turn yields a better running time than was previously known for a sequential algorithm to solve this problem. The previous best sequential running time for PSPM in R 3 is O (kn 5/2 [λ 6 (n)/n] 1/4 log n) time, where k is the size of the pattern and n is the size of the sample set. In the current paper, we show that a sequential algorithm can solve PSPM in R 3 in O (kn 2 [λ 6 (n)/n] 1/2 log n) time.