Fast pattern matching for entropy bounded text

Abstract

We present the first known case of one-dimensional and two-dimensional string matching algorithms for text with bounded entropy. Let n be the length of the text and m be the length of the pattern. We show that the expected complexity of the algorithms is related to the entropy of the text for various assumptions of the distribution of the pattern. For the case of uniformly distributed patterns, our one dimensional matching algorithm works in O(nlogm/(pm)) expected running time where H is the entropy of the text and p=1-(1-H/sup 2/)/sup H/(1+H)/. The worst case running time T can also be bounded by (n log m/p(m+/spl radic/V))/spl les/T/spl les/(n log m/p(m-/spl radic/V)) if V is the variance of the source from which the pattern is generated. Our algorithm utilizes data structures and probabilistic analysis techniques that are found in certain lossless data compression schemes.