Do we really need to balance patricia tries?
In this paper, we give exact and asymptotic approximations for the variance of the external path length in a symmetric Patricia trie. The problem was open up to now. We prove that for the binary Patricia trie, the variance is asymptotically equal to 0.37 ... n+n P (log2n) where n is the number of stored records and P(x) is a periodic function with a very small amplitude. This result is next used to show that from the practical (average) viewpoint, the Patricia trie does not need to be restructured in order to keep it balanced. In general, we ask to what extent simpler and more direct algorithms (for digital search tries) can be expected in practice to match the performance of more complicated, worst-case asymptotically better ones.
KeywordsInternal Node Probability Generate Function External Node Complete Binary Tree Left Subtree
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