Two-dimensional pattern matching with rotations

Authors:
Amihood Amir;Ayelet Butman;Maxime Crochemore;Gad M. Landau;Mary Schaps
Affiliations:
Department of Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel and Georgia Tech;Department of Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel;Institut Gaspard-Monge, University of Marne-La-Vallée, London, UK and King's College, London, UK;Department of Computer Science, Haifa University, Haifa 31905, Israel and Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY;Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different possible rotated patterns. Subsequently, given an m × m array (pattern) and an n × n array (text) over some finite alphabet Σ, we present a new method yielding an O(n2m3) time algorithm for this problem.