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Optimal Path-Decomposition of Tries

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daigle_alexandre.pdf (684.52 KB)

Date

2016-05-16

Authors

Daigle, Alexandre

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Publisher

University of Waterloo

Abstract

In this thesis, we consider the path-decomposition representation of prefix trees. We show that given query probabilities for every word in the prefix tree, the heavy-path strategy produces the optimal trie with respect to the number of node accesses. We show how to implement the heavy-path strategy in O(N) time for a trie containing n words with total length N. To prove this result, we show a complete characterization of the choices made by the optimal decomposition strategy. Using this characterization, we describe how to efficiently support dynamic operations on the path-decomposed trie while preserving the optimality in O(sigma * |w|) time for an alphabet size of sigma and a word length of |w|. We also give entropy-based bounds of the node accesses per query for their respective probabilities. Finally, we show theoretical and experimental results on the performance of heavy-path versus max-score, another popular path-decomposition strategy.

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Keywords

Auto-completion, Path-Decomposed Trie, Optimal, Data Structure, Prefix Tree, Heavy-Path

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URI

http://hdl.handle.net/10012/10491

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Theses
Computer Science