Two-Dimensional Periodicity in Rectangular Arrays

Abstract. String matching is rich with a variety of algorithmic tools. In contrast, multidimensional matching has had a rather sparse set of techniques. This paper presents a new algorithmic technique for two-dimensional matching: periodicity analysis. Its strength appears to lie in the fact that it is inherently two-dimensional. Periodicity in strings has been used to solve string matching problems. Multidimensional periodicity, however, is not as simple as it is in strings and was not formally studied or used in pattern matching. In this paper, we define and analyze two-dimensional periodicity in rectangular arrays. One definition of string periodicity is that a periodic string can self-overlap in a particular way. An analogous concept is true in two dimensions. The self-overlap vectors of a rectangle generate a regular pattern of locations where the rectangle may originate. Based on this regularity, we define four categories of periodic arrays—nonperiodic, lattice periodic, lin...

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Amihood Amir, Gary Benson
• Keywords: Algorithm, SIAMCOMP 1998, String Matching, Two-dimensional