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A new, momentum preserving fast Poisson solver for N-body systems sharing effective O(N) computational complexity, has been recently developed by Dehnen (2000, 2002). We have implemented the proposed algorithms in a Fortran-90 code, and…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
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…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…
On-shell constructibility is redefining our understanding of perturbative quantum field theory. The tree-level S-matrix of constructible theories is completely determined by a set of recurrence relations and a reduced number of scattering…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
The rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a well-studied measure of topological dissimilarity that is NP-hard to compute. Here we describe an improved linear kernel for the problem.…
We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node $t$ in a given tree $T$. Upon querying a node $v$ of the tree, the strategy receives as a reply an…
Segmentation-based image coding methods provide high compression ratios when compared with traditional image coding approaches like the transform and sub band coding for low bit-rate compression applications. In this paper, a…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
Herein we explore a dual tree algorithm for matrix multiplication of $A\in \mathbb{R}^{M\times D}$ and $B\in\mathbb{R}^{D\times N}$, very narrowly effective if the normalized rows of $A$ and columns of $B$, treated as vectors in…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
We consider the following generalization of binary search in sorted arrays to tree domains. In each step of the search, an algorithm is querying a vertex $q$, and as a reply, it receives an answer, which either states that $q$ is the…
In models to generate program source code from natural language, representing this code in a tree structure has been a common approach. However, existing methods often fail to generate complex code correctly due to a lack of ability to…
We present an implementation of the hierarchical tree algorithm on the individual timestep algorithm (the Hermite scheme) for collisional $N$-body simulations, running on GRAPE-9 system, a special-purpose hardware accelerator for…
Approximate nearest neighbour (ANN) search is one of the most important problems in computer science fields such as data mining or computer vision. In this paper, we focus on ANN for high-dimensional binary vectors and we propose a simple…
Gadget3 is nowadays one of the most frequently used high performing parallel codes for cosmological hydrodynamical simulations. Recent analyses have shown t\ hat the Neighbour Search process of Gadget3 is one of the most time-consuming…
Huffman coding is a widely used method for lossless data compression because it optimally stores data based on how often the characters occur in Huffman trees. An $n$-ary Huffman tree is a connected, cycle-lacking graph where each vertex…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and…