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The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
This paper presents a batch classifier that has been improved from the earlier version and fixed a mistake in the earlier paper. Two important changes have been made. Each category is represented by a classifier, where each classifier…
We study the distributed detection problem in a balanced binary relay tree, where the leaves of the tree are sensors generating binary messages. The root of the tree is a fusion center that makes the overall decision. Every other node in…
We revisit weight-balanced trees, also known as trees of bounded balance. This class of binary search trees was invented by Nievergelt and Reingold in 1972. Such trees are obtained by assigning a weight to each node and requesting that the…
Various networks are broadly and deeply applied in real-life applications. Reliability is the most important index for measuring the performance of all network types. Among the various algorithms, only implicit enumeration algorithms, such…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
In this paper two new graph operations are introduced, and with them the S-trees are studied in depth. This allows to find \(\{-1,0,1\}\)-basis for all the fundamental subspaces of the adjacency matrix of any tree, and to understand in…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…
This paper presents the first implementation of a search tree data structure in an asynchronous shared-memory system that provides a wait-free algorithm for executing range queries on the tree, in addition to non-blocking algorithms for…
The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining,…
We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…
Learning vector representations for programs is a critical step in applying deep learning techniques for program understanding tasks. Various neural network models are proposed to learn from tree-structured program representations, e.g.,…
The size of the largest common subtree (maximum agreement subtree) of two independent uniform random binary trees on $n$ leaves is known to be between orders $n^{1/8}$ and $n^{1/2}$. By a construction based on recursive splitting and…
Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data…
The supertree problem asking for a tree displaying a set of consistent input trees has been largely considered for the reconstruction of species trees. Here, we rather explore this framework for the sake of reconstructing a gene tree from a…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…
As data volumes continue to grow rapidly, traditional search algorithms, like the red-black tree and B+ Tree, face increasing challenges in performance, especially in big data scenarios with intensive storage access. This paper presents the…
We study some essential arithmetic properties of a new tree-based number representation, {\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant…