Summary: Two­Dimensional Periodicity in Rectangular Arrays \Lambda
Amihood Amir y
College of Computing
Georgia Institute of Technology
amir@cc.gatech.edu
Gary Benson y
Department of Biomathematical Sciences
Mount Sinai School of Medicine
benson@ecology.biomath.mssm.edu
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 two­dimensional matching: periodicity analysis. Its strength appears to lie in the
fact that it is inherently two­dimensional.
Periodicity in strings has been used to solve string matching problems. Multidimensional
periodicity, though, 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 two­dimensional periodicity in rectan­
gular arrays. One definition of string periodicity is that a periodic string can self­overlap 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

Source: Amir, Amihood - Computer Science Department, Bar Ilan University

Collections: Mathematics