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Publication# Fast And Space Efficient Trie Searches

2000

Report or working paper

Report or working paper

Abstract

Searching and traversing m-way trees using tries is a well known and broadly used technique. Three algorithms are presented, two have constant insert, search and delete cost, are faster than Hash Trees and can be searched twice as quickly cas Ternary Search Trees (TST). The third has a lg(N) byte compare cost like a TST, but is faster. All require 60% less memory space per node than TST and, unlike Hash Trees, are smoothly extensible and support sorted order functions. The new algorithms defining Array Compacted Trees (ACT), Array Mapped Trees (AMT), Unary Search Trees (UST) and their variants are discussed. These new search trees are applicable in many diverse areas such as high performance IP routers, symbol tables, lexicon scanners and FSA state tables.

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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 result is that the number of children of every internal node is at most the radix r of the radix tree, where r is a positive integer and a power x of 2, having x ≥ 1. Unlike regular trees, edges can be labeled with sequences of elements as well as single elements.

Trie

In computer science, a trie (ˈtriː, ˈtraɪ), also called digital tree or prefix tree, is a type of k-ary search tree, a tree data structure used for locating specific keys from within a set. These keys are most often strings, with links between nodes defined not by the entire key, but by individual characters. In order to access a key (to recover its value, change it, or remove it), the trie is traversed depth-first, following the links between nodes, which represent each character in the key.

Binary tree

In computer science, a binary tree is a k-ary tree data structure in which each node has at most two children, which are referred to as the and the . A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences.

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