E = I + T: The internal extent formula for compacted tries
Data Structures and Algorithms
2010-12-15 v1 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.1012.3024,
title = {E = I + T: The internal extent formula for compacted tries},
author = {Paolo Boldi and Sebastiano Vigna},
journal= {arXiv preprint arXiv:1012.3024},
year = {2010}
}