It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

Through their recursive definition, many fractals have an inherent hierarchical structure. An example are binary branching Pythagoras Trees. By stopping the recursion in certain branches, a binary hierarchy can be encoded and visualized. But this binary encoding is an obstacle for representing general hierarchical data such as file systems or phylogenetic trees, which usually branch into more t...

In a graph theory model, clustering is the process of division of vertices into groups, with a higher density of edges within groups than between them. In this paper, we introduce a new clustering method for detecting such groups and use it to analyse some classic social networks. The new method has two distinguished features: non-binary hierarchical tree and the feature of overlapping clusteri...

We develop a new method for building a hierarchical tree from binary sequence data. It is based on an ancestral mixture model. The sieve parameter in the model plays the role of time in the evolutionary tree of the sequences. By varying the sieve parameter, one can create a hierarchical tree that estimates the population structure at each fixed backward point in time. Application to the cluster...

An adaptive hierarchical structure called ‘‘Binary Tree TASOM’’ (BTASOM) is proposed, which resembles a binary natural tree having nodes composed of Time Adaptive Self-Organizing Map (TASOM) networks. The standard TASOM is almost as slow as the standard SOM and has a fixed number of neurons. The BTASOM is proposed to make the TASOM fast and adaptive in the number of its neurons. The BTASOM is t...

Hierarchical bit vectors represent sets of integers using a collection of bit vectors. At the top level, a single bit is set iff the set is non-empty. The bits of this next level summarize ranges of the elements. In the case of a binary hierarchical bit vector the two bits of the next level summarize two ranges: the lower half and the upper half of the possible elements. At the lowest level eac...

This paper proposes an intelligent approach for dynamic identification of the vehicles. The proposed approach is based on the data-driven identification and uses a high-performance local model network (LMN) for estimation of the vehicle’s longitudinal velocity, lateral acceleration and yaw rate. The proposed LMN requires no pre-defined standard vehicle model and uses measurement data to identif...

This paper introduces the arc tree, a hierarchical data structure to represent arbitrary curved shapes. The arc tree is a balanced binary tree that represents a curve of length 1 such that any subtree whose root is on the kth tree level is representing a subcurve of length 1/2k. Each tree level is associated with an approximation of the curve; lower levels correspond to approximations of higher...

In this short paper, we propose a new key management architecture for Multicast communications. This architecture combines the complementary variable approach with hashed keys and hierarchical binary trees. This will reduce the number of transmissions at the joins/leaves of participants. Also, we explain a naming method, which allows to facilitate the understanding of the hierarchical binary tr...