Abstract
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 k, 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((nlogk n)/B) disk pages and finds all k-error matches with \(O((|P|+occ)/B + \log^k n \log \log_{\scriptscriptstyle B} n)\) 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 \(\Omega(|P| + occ + \mbox{poly}(\log n))\) I/Os. The second index reduces the space to O((nlogn)/B) disk pages, and the I/O complexity is O((|P| + occ)/B + logk(k + 1) n loglogn).
Research of T.W. Lam is supported by the Hong Kong RGC Grant 7140/06E. Research of R. Shah and J.S. Vitter is supported by NSF Grants IIS–0415097 and CCF–0621457, and ARO Grant DAAD 20–03–1–0321. Part of the work was done while W.K. Hon was at Purdue University.
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Hon, WK., Lam, TW., Shah, R., Tam, SL., Vitter, J.S. (2007). Cache-Oblivious Index for Approximate String Matching. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_7
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