A unifying framework for trie design heuristics

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Abstract

A general framework for the design of tries with various cost functions is presented. A systematic procedure is proposed which is analogous to the information theoretic heuristic in the use of uncertainty-based information measures. For any file of records to be retrieved by means of keys arranged in a trie, an uncertainty measure must constitute a lower bound on the cost of any trie associated with the file. A trie can be constructed by selecting as the next key to be tested the key that maximizes the information per unit cost based on the uncertainty measure chosen. This stepwise heuristic for constructing tries can be applied to arbitrary cost functions, and it is shown that these information measures possess properties similar to those from information theory. The technique is applied to the problem of constructing tries for the r-error digital search problem which deals with locating the binary word in a file that matches a given input word, while taking into account that as many as r digits of the input may be erroneous.

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