Cache-Oblivious Index for Approximate String Matching

摘要

This paper revisits the problem of indexing a text for approximate string matching. Specifically, given a text T of length n and a positive integer κ, we want to construct an index of T such that for any input pattern P, we can find all its k-error matches in T efficiently. This problem is well-studied in the internal-memory setting. Here, we extend some of these recent results to external-memory solutions, which are also cache-oblivious. Our first index occupies O((n log~κ n)/B) disk pages and finds all k-error matches with O((|P| + occ)/B + log~κ n log log _B n) I/Os, where B denotes the number of words in a disk page. To the best of our knowledge, this index is the first external-memory data structure that does not require Ω(|P| + occ + poly(log n)) I/Os. The second index reduces the space to O((n log n)/B) disk pages, and the I/O complexity is O((|P| + occ)/B + log~(κ(κ+1)) n log log n).