Use of tree structures for processing files

Abstract

In data processing problems, files are frequently used which must both be searched and altered. Binary search techniques are efficient for searching large files, but the associated file organization is not readily adapted to the file alterations. Conversely, a chained file allocation permits elcient alteration but cannot be searched efficiently. A file organized into a tree-like structure is discussed, and it is shown that such a file may both be searched and altered with times proportional to s log, N , where N is the number of file items and s is a parameter of the tree. It is also shown that optimizing the value of s leads to a search time which is only 25 per cent slower than the binary search. The tree organization employs two data chains and may be considered to be a compromise between the organizations for the binary search and the chained file. The relation of the tree organization to multidimensional indexing and to the trie structure is also discussed.

Burst tries

“…That is, the search cost is bounded by the length of the query string. With a small increase in complexity of implementation, a trie can be substantially reduced in size by omitting nodes that lead to a single leaf [46]. In such a trie, chains that lead to a leaf without branching are eliminated; we refer to this variant as a compact trie.…”

“…A burst trie can be viewed as a generalisation of other proposed variants of trie [49,40,46], as discussed later. Figure 1 shows an example of a burst trie storing ten records whose keys are "came", "car", "cat", "cave", "cy", "cyan", "we", "went", "were", and "west" respectively.…”

“…However, the space savings come at the expense of a linked list traversal in each node instead of a simple array lookup [43]. Sussenguth [46] proposed a modified form of the linked list implementation of a trie, called a double-chained tree, in which all children of a node are placed in a list as in the linked-list implementation explained above. In addition, each list node contains a pointer to a list of its children.…”

“…Based on theoretical analysis of a list trie, Sussenguth has suggested that the expected search time can be minimised when list trie nodes stop branching when there are less than six keys. Instead of a further branching the keys should be kept directly in the node in a linked list where they can be sequentially accessed [46]. However, the analysis concerns a slow variant of tries and cannot be applied to array tries.…”

“…A simple way to reduce the number of trie nodes is to omit chains of nodes that have only a single descendant and lead to a leaf. This variant of a trie, in which tailing "sticks" caused by single-descendant nodes are eliminated [46], we refer to as a compact trie; we use the array implementation of a compact trie in our experiments.…”