Least Random Suffix/Prefix Matches in Output-Sensitive Time

Abstract

We study the problem of finding suffix/prefix matches (overlaps) when given a set of r strings of total length n. Gusfield et al. (1992) gave an algorithm to find the longest exact overlaps between all string-pairs in the optimal O(n + t _o utput) time, where t _o utput ≤ r ² is the number of non-zero length overlaps found. So far the best worst-case time for finding approximate overlaps within edit distance k has been O(knr) (Landau et al. 1998), which gives Ω(r ²) time regardless of the output size. We propose the first output-sensitive algorithm to find either the longest or the least random approximate overlaps. Given the maximum edit distance k allowed in an overlap, the approximate overlaps can be found in linear space and in O((n + t _o utput) polylog(n)) time for any constant k. If all input strings are shorter than \(\log n/(k^\frac{1}{k}\sigma)\), we achieve the time complexity O(n log ^k n + t _o utput) for any k. For strings longer than εlog ^k r, we improve the previous best worst-case time from O(knr) to \(O(\frac{c^k}{k!}nr)\) for moderate k and constants c > 1 and ε > 0.