Radix tree

In computer science, a radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which each node that is the only child is merged with its parent. The number of children of every internal node is at most the radix r of the radix tree, where r = 2x for some integer x ≥ 1. Unlike regular trees, edges can be labeled with sequences of elements as well as single elements. This makes radix trees much more efficient for small sets (especially if the strings are long) and for sets of strings that share long prefixes.

Unlike regular trees (where whole keys are compared en masse from their beginning up to the point of inequality), the key at each node is compared chunk-of-bits by chunk-of-bits, where the quantity of bits in that chunk at that node is the radix r of the radix trie. When r is 2, the radix trie is binary (i.e., compare that node's 1-bit portion of the key), which minimizes sparseness at the expense of maximizing trie depth—i.e., maximizing up to conflation of nondiverging bit-strings in the key. When r ≥ 4 is a power of 2, then the radix trie is an r-ary trie, which lessens the depth of the radix trie at the expense of potential sparseness.

As an optimization, edge labels can be stored in constant size by using two pointers to a string (for the first and last elements).

Note that although the examples in this article show strings as sequences of characters, the type of the string elements can be chosen arbitrarily; for example, as a bit or byte of the string representation when using multibyte character encodings or Unicode.

Applications

Radix trees are useful for constructing associative arrays with keys that can be expressed as strings.