Geometric Point Pattern Matching in the Knuth-Morris-Pratt Way

Esko Ukkonen (University of Helsinki, Finland)

Abstract: Given finite sets P and T of points in the Euclidean space R^d, the point pattern matching problem studied in this paper is to find all translations f ∈ R^d such that P + f ⊆ T. A fast search algorithm with some variants is presented for point patterns P that have regular grid-like geometric shape. The algorithm is analogous to the Knuth-Morris-Pratt algorithm of string matching. The time requirement of the search is O(r|T|) where r is the grid dimension of P. Pattern P has grid dimension r = 1 if it consists of evenly spaced points on a line. In general, a pattern P is an r-dimensional grid if it has for some p ∈ P and e1, ... , e_r ∈ R^d and positive integers m₁, ... , m_r a representation P = {p + i₁e₁ + ⋅⋅⋅ + i_re_r | 0 ≤ i_j ≤ m_j} where the i_j's are integers. Both P and T are given to the search algorithm in the lexicographic order.

Keywords: Knuth-Morris-Pratt algorithm, pattern matching, point sets, translation,

Categories: F.2, I.3, I.7