O(k) Parallel Algorithms for Approximate String Matching Approximate String Matching (proposed Running Head)

Given a text string T of length n, a shorter pattern string A of length m, and an integer k, an simple straightforward O(k) parallel algorithm for nding all occurrences of the pattern string in the text string with at most k di erences (as de ned by edit distance) is presented. The algorithm uses the priority CRCW-PRAM model of computation and (n m+ k + 2) m = O(n m) processors. Over recent decades, the k-di erences string matching problem received much attention in the research literature, due to its importance in molecular biology, text retrieval, and other types of applications. Based on a variation of Ukkonen's algorithm, this paper presents several di erent ways of achieving a time complexity of O(k) for solving this problem with di erent CRCW-PRAM assumptions.