Generation, Ranking and Unranking of Ordered Trees with Degree Bounds

M. Amani, A. Nowzari-Dalini
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引用次数: 5

Abstract

We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in which no node has degree greater than 4. By allowing up to $\Delta$ children for each node of chemical tree instead of 4, we will have a generalization of chemical trees. Here, we introduce a new encoding over an alphabet of size 4 for representing unlabeled ordered trees with maximum degree of $\Delta$. We use this encoding for generating these trees in A-order with constant average time and O(n) worst case time. Due to the given encoding, with a precomputation of size and time O(n^2) (assuming $\Delta$ is constant), both ranking and unranking algorithms are also designed taking O(n) and O(nlogn) time complexities.
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有度界的有序树的生成、排序和取消排序
研究了节点最大度为$\Delta$的无标记有序树的生成、排序和取消排序问题。这类树代表了化学树的一种概括。化学树是一棵未标记的树,其中没有节点的度数大于4。通过为化学树的每个节点允许最多$\Delta$子节点,而不是4个,我们将有一个化学树的泛化。这里,我们在大小为4的字母表上引入一种新的编码,用于表示最大程度为$\Delta$的未标记有序树。我们使用这种编码以a阶生成这些树,平均时间为常数,最坏情况为O(n)。由于给定的编码,预计算的大小和时间为O(n^2)(假设$\Delta$为常数),排序和不排序算法也被设计为O(n)和O(nlogn)时间复杂度。
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