E=I+T: The internal extent formula for compacted tries

Authors:
Paolo Boldi;Sebastiano Vigna
Affiliations:
Universití degli Studi di Milano, Italy;Universití degli Studi di Milano, Italy
Venue:
Information Processing Letters
Year:
2011

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Abstract

It is well known (Knuth, 1997 [5, pp. 399-400]) that in a binary tree the external path length minus the internal path length is exactly 2n-2, where n is the number of external nodes. We show that a generalization of the formula holds for compacted tries, replacing the role of paths with the notion of extent, and the value 2n-2 with the trie measure, an estimation of the number of bits that are necessary to describe the trie.