Fast average-case pattern matching by multiplexing sparse tables

Abstract

Pattern matching consists of finding occurrences of a pattern in some data. One general approach is to sample the data collecting evidence about possible matches. By sampling appropriately, we force matches to be sparse and can encode a table of size m as a series of smaller tables with total size Θ( (ln m) 2 ln ln m ) . This method yields practical algorithms with fast average-case running times for a wide variety of pattern matching and pattern recognition problems. We apply our technique of multiplexing sparse tables to the k-mismatches string searching problem which asks for all occurrences of a pattern string P = p 0, p 1, …, p m-1 , in a text string T = t 0, t 1, …, n-1 , with ⩽ k mismatches (substitutions) where P, T and k are given. Assuming a uniform character distribution over an alphabet of size A, for k⩽ m/(2 log A m), our algorithm has an average-case running time of Θ(kn (log m) 2 (m log log m) ) and uses Θ(m (log m) 2 (log log m) ) space.