Related papers: Tree Embedding in High Dimensions: Dynamic and Mas…
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
Tree edit distance is a well-studied measure of dissimilarity between rooted trees with node labels. It can be computed in $O(n^3)$ time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007], and fine-grained hardness results suggest that the…
It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
An oblivious subspace embedding is a random $m\times n$ matrix $\Pi$ such that, for any $d$-dimensional subspace, with high probability $\Pi$ preserves the norms of all vectors in that subspace within a $1\pm\epsilon$ factor. In this work,…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
The M-tree is a paged, dynamically balanced metric access method that responds gracefully to the insertion of new objects. To date, no algorithm has been published for the corresponding Delete operation. We believe this to be non-trivial…
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…
Given a set $P$ of $n$ points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…
We introduce an algorithm that performs a one-directional mesh overset of a parallel forest of octrees with another distributed mesh of unrelated partition. The forest mesh consists of several adaptively refined octrees. Individual smooth…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 47:15--32, 2015]) are compact indices for texts over an alphabet $[0,\sigma)$ that support rank, select and access queries in $O(\lg \sigma)$ time.…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
The growing complexity of spatial and structural information in 3D data makes data inspection and visualization a challenging task. We describe a method to create a planar embedding of 3D treelike structures using their skeleton…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
The problem of embedding a set of objects into a low-dimensional Euclidean space based on a matrix of pairwise dissimilarities is fundamental in data analysis, machine learning, and statistics. However, the assumptions of many standard…