Ranking and Unranking Algorithm for Neuronal Trees in B-order

Abstract

In this paper, we present two new ranking and unranking algorithms for neuronal trees in B-order. These algorithms are based on a generation algorithm which is given for integer sequences corresponding to neuronal trees by Pallo. A neuronal tree is a rooted tree with n external nodes (leaves) whose internal nodes have at least two children. These trees are used in computational neuroscience for modeling the connections between neurons in brain, and are also called neuronal dendritic trees. Up to our knowledge no other ranking and unranking algorithms are given for integer sequences corresponding to neuronal trees in B-order. The time complexity of the presented ranking and unranking algorithms for neuronal trees with n leaves are O(n) and O(n log n), respectively.