Improved Practical Compact Dynamic Tries

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.