Randomized Ternary Search Tries

TL;DR

This paper introduces a self-balancing ternary search trie using a randomized strategy inspired by treaps, ensuring efficient search, insertion, and deletion operations with high probability.

Contribution

It presents a novel randomized balancing method for ternary search tries, combining ideas from treaps to achieve probabilistic efficiency guarantees.

Findings

Search, insert, delete operations run in O(k + log n) time with high probability.

The data structure maintains balanced properties after arbitrary insertions and deletions.

Performance is comparable to balanced binary search trees but for ternary tries.

Abstract

This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of strings, the tree looks like a ternary search trie built by inserting strings in random order. As a result, the time cost of searching, inserting, or deleting a string of length k in a tree with n strings is at most O(k + log n) with high probability.