Abstract
We consider the problem of implementing a dynamic trie with an emphasis on good practical performance. For a trie with n nodes with an alphabet of size \(\sigma \), the information-theoretic lower bound is \(n \log \sigma + O(n)\) bits. The Bonsai data structure [1] supports trie operations in O(1) expected time (based on assumptions about the behaviour of hash functions). While its practical speed performance is excellent, its space usage of \((1+\epsilon ) n (\log \sigma + O(\log \log n))\) bits, where \(\epsilon \) is any constant \(> 0\), is not asymptotically optimal. We propose an alternative, m-Bonsai, that uses \((1 + \epsilon ) n (\log \sigma + O(1))\) bits in expectation, and supports operations in O(1) expected time (again based on assumptions about the behaviour of hash functions). We give a heuristic implementation of m-Bonsai which uses considerably less memory and is slightly faster than the original Bonsai.
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Poyias, A., Raman, R. (2015). Improved Practical Compact Dynamic Tries. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds) String Processing and Information Retrieval. SPIRE 2015. Lecture Notes in Computer Science(), vol 9309. Springer, Cham. https://doi.org/10.1007/978-3-319-23826-5_31
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