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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