# A Boyer-Moore Approach for Two-Dimensional Matching

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/CSD-93-784.pdf

A 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 = [log_c( rm)]. The expected running time of the algorithm is shown to be O( n^2 [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.

BibTeX citation:

```@techreport{Tarhio:CSD-93-784,
Author = {Tarhio, Jorma},
Title = {A Boyer-Moore Approach for Two-Dimensional Matching},
Institution = {EECS Department, University of California, Berkeley},
Year = {1993},
Month = {Dec},
URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/6322.html},
Number = {UCB/CSD-93-784},
Abstract = {A simple sublinear algorithm is presented for two-dimensional string matching, where occurrences of a pattern of <i>m</i> x <i>m</i> characters are searched for in a text of <i>n</i> x <i>n</i> characters in an alphabet of <i>c</i> characters. The algorithm is based on the Boyer-Moore idea and it examines a strip of <i>r</i> columns at a time, <i>m</i>/2 <= <i>r</i> <= <i>m</i>. The shift of the pattern is based on a string of <i>d</i> characters, <i>d</i> = [log_c(<i>rm</i>)].  The expected running time of the algorithm is shown to be <i>O</i>(<i>n</i>^2 [log_c<i>m</i>^2] / <i>m</i>^2 + <i>cm</i>^2) for random texts and patterns. The algorithm is easy to implement, and results of experiments are reported to show its practical efficiency.}
}
```

EndNote citation:

```%0 Report
%A Tarhio, Jorma
%T A Boyer-Moore Approach for Two-Dimensional Matching
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/CSD-93-784
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/6322.html
%F Tarhio:CSD-93-784
```