Efficient Parallel And Serial Approximate String Matching

Consider the string matching problem, where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern or a superfluous character in the text or a superfluous character in the pattern. Given a text of length n, a pattern of length m and an integer k, we present parallel and serial algorithms for finding all occurrences of the pattern in the text with at most k differences. The first part of the parallel algorithm consists of analysis of the pattern and takes O(log m) time using m 2 processors. The rest of the algorithm consists of handling the text. The text handling part applies the following new approach. This part starts by obtaining a concise characterization of the text which is based solely on substrings of the pattern in O(log m) time using n / log m processors. Then the desired output is derived from this characterization together with the tables built in the first part in O(k) time using n processors. The serial algorithm follows also this new approach for handling the text. It runs in O(kn) time for alphabet whose size is fixed. For general input the algorithm requires O(n(k + log m) ) time. In both cases the space requirement is O(n).