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.
E=I+T: The internal extent formula for compacted tries / P. Boldi, S. Vigna. - In: INFORMATION PROCESSING LETTERS. - ISSN 0020-0190. - 111:7(2011), pp. 310-313. [10.1016/j.ipl.2010.12.012]
E=I+T: The internal extent formula for compacted tries
P. BoldiPrimo
;S. VignaUltimo
2011
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.
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