Randomized Ternary Search Tries

A simple method for maintaining balance in ternary search tries is presented. The new kind of self-balancing ternary search trie, called an r-trie, generalizes the balancing strategy of Aragon and Seidel’s randomized binary search trees (treaps). This means that an r-trie is shaped like a ternary search trie built by inserting the strings in random order. As a result, the time cost of searching, inserting, or deleting a string of length k in an r-trie for n strings is in O(k + log n) with high probability.