Improved Practical Compact Dynamic Tries

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 $$n \\log \\sigma + On$$ bits. The Bonsai data structure [1] supports trie operations in O1 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 $$1 + \\epsilon n \\log \\sigma + O1$$ bits in expectation, and supports operations in O1 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.