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

It is well known 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.

preprint2010arXivOpen access
Paolo BoldiSebastiano Vigna
Data Structures and AlgorithmsDiscrete Mathematics
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Paolo BoldiSebastiano Vigna

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