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 σ, the information-theoretic lower bound is nlogσ+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+ϵ)n(logσ+O(loglogn)) bits, where ϵ is any constant >0, is not asymptotically optimal. We propose an alternative, m-Bonsai, that uses (1+ϵ)n(logσ+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.