Gap terminology and related combinatorial properties for AVL trees and Fibonacci-isomorphic trees

Amani, Mahdi

doi:10.1016/j.akcej.2018.01.019

Cited by 3 publications

(2 citation statements)

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“…For example, the x-sequence and z-sequence codewords of the (2, 3)-ary of Figure 1 are x = (10000001001100000000000000) and z = (1,8,11,12).…”

Section: Encoding and Generation Algorithmmentioning

confidence: 99%

“…The problem of generating trees, as one of the most important combinatorial objects, has been thoroughly investigated in the literature and many papers have been published which deal with the generation of these objects. For example, we can mention the generation of binary trees in [2,3,28,29], k-ary trees in [4,11,13,20,21,22,31],trees with n nodes and m leaves in [17,23], neuronal trees in [5,6,18,27], non-regular trees in [30], bounded ordered trees in [7], Fibonacci-isomorphic trees in [8], and AVL trees in [15].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Generation, Ranking, and Unranking of (k, m)-Ary Trees in B-Order

Amani

Nowzari-Dalini

2018

Bull. Iran. Math. Soc.

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In this paper, we present a new generation algorithm with corresponding ranking and unranking algorithms for (k, m)-ary trees in B-order. (k, m)-ary tree is introduced by Du and Liu. A (k, m)-ary tree is a generalization of k-ary tree whose every node of even level of the tree has degree k and odd level of the tree has degree 0 or m. Up to our knowledge no generation, ranking or unranking algorithms are given in the literature for this family of trees. We use Zaks' encoding for representing (k, m)-ary trees, and to generate them in B-order. We also prove that, to generate (k, m)-ary trees in B-order using this encoding, the corresponding codewords should be generated in reverse-lexicographical ordering. The presented generation algorithm has a constant average time and O(n) time complexity in the worst case. Due to the given encoding, both ranking and unranking algorithms are also presented taking O(n) and O(n log n) time complexity, respectively.

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“…For example, the x-sequence and z-sequence codewords of the (2, 3)-ary of Figure 1 are x = (10000001001100000000000000) and z = (1,8,11,12).…”

Section: Encoding and Generation Algorithmmentioning

confidence: 99%