Abstract
In the approximate dictionary search problem we have to construct a data structure on a set of strings so that we can answer to queries of the kind: find all strings of the set that are similar (according to some string distance) to a given string. In this paper we propose the first data structure for approximate dictionary search that occupies optimal space (up to a constant factor) and able to answer an approximate query for edit distance “1” (report all strings of dictionary that are at edit distance at most “1” from query string) in time linear in the length of query string. Based on our new dictionary we propose a full-text index for approximate queries with edit distance “1” (report all positions of all sub-strings of the text that are at edit distance at most “1” from query string) answering to a query in time linear in the length of query string using space \(O(n(\lg(n)\lg\lg(n))^2)\) in the worst case on a text of length n. Our index is the first index that answers queries in time linear in the length of query string while using space O(n·poly(log(n))) in the worst case and for any alphabet size.
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Belazzougui, D. (2009). Faster and Space-Optimal Edit Distance “1” Dictionary. In: Kucherov, G., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 2009. Lecture Notes in Computer Science, vol 5577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02441-2_14
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DOI: https://doi.org/10.1007/978-3-642-02441-2_14
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