Two and higher dimensional pattern matching in optimal expected time
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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An simple sublinear algorithm is presented for two-dimensional string matching, where occurrences of a pattern of m x m characters are searched for in a text of n x n characters in an alphabet of c characters. The algorithm is based on the Boyer-Moore idea and it examines a strip of r columns at a time, m/2 = r = m. The shift of the pattern is based on a string of d characters, d=ceiling(log_c(rm)). The expected running time of the algorithm is shown to be O(n^2 ceiling(log_c(m^2))/m^2+cm^2) for random texts and patterns. The algorithm is easy to implement, and results of experiments are reported to show its practical efficiency.