Fast approximate dictionary matching

Abstract

In the approximate dictionary matching problem, a dictionary that contains a set of pattern strings is given. The user presents a text string and a tolerance k (k is a positive integer) and asks for all occurrences of all dictionary patterns that appear in the text with at most k differences to the original patterns. We present two algorithms for the problem. The first algorithm assumes that all patterns in the dictionary are of the same length. The second algorithm removes this assumption at the expense of a bit more complicated preprocess of the dictionary and slower query time. The basic idea behind our algorithms is to represent each dictionary pattern with one or two points in a ¦Σ¦ ^q — dimensional real space under the L ₁-metric where Σ is the underlying alphabet and q a fixed integer and then organize these points with some spatial data structure to make subsequent searches with different texts of different lengths and different tolerance values fast. Although the approximate dictionary matching would be of enormous importance in molecular biological applications, no previous results for the problem are known.