Compressed String Dictionary Search with Edit Distance One

In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern (Formula presented.) , the index has to report all the strings in the dictionary having edit distance at most one with (Formula presented.). Our first solution is able to solve queries in (almost optimal) (Formula presented.) time where (Formula presented.) is the number of strings in the dictionary having edit distance at most one with (Formula presented.). The space complexity of this solution is bounded in terms of the (Formula presented.) th order entropy of the indexed dictionary. A second solution further improves this space complexity at the cost of increasing the query time. Finally, we propose randomized solutions (Monte Carlo and Las Vegas) which achieve simultaneously the time complexity of the first solution and the space complexity of the second one