Abstract
In this work, we focus on building an efficient succinct dynamic dictionary that significantly improves the query time of the current best known results. The algorithm that we propose suffers from only a \( O((\log \log n)^2 )\) multiplicative slowdown in its query time and a \(O(\frac{1}{\epsilon } \log n)\) slowdown for insertion and deletion operations, where n is the sum of all of the patterns’ lengths, the size of the alphabet is \(\textit{polylog}(n)\) and \(\epsilon \in (0,1)\). For general alphabet the query time is \( O((\log \log n) \log \sigma )\), where \(\sigma \) is the size of the alphabet. A byproduct of this paper is an Aho-Corasick automaton that can be constructed with only a compact working space, which is the first of its type to the best of our knowledge.
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Notes
\(O(|T| + n + occ)\) when using hashing.
Any other non succinct algorithm that requires up to \(O(\log \log n)\) query and update time can be used.
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This research was supported by the Kabarnit Cyber consortium funded by the Chief Scientist in the Israeli Ministry of Economy under the Magnet Program.
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Feigenblat, G., Porat, E. & Shiftan, A. A Grouping Approach for Succinct Dynamic Dictionary Matching. Algorithmica 77, 134–150 (2017). https://doi.org/10.1007/s00453-015-0056-0
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DOI: https://doi.org/10.1007/s00453-015-0056-0