Related papers: New Algorithms on Wavelet Trees and Applications t…

This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…

We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…

Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…

The need for scalable concurrent ordered set data structures with linearizable range query support is increasing due to the rise of multicore computers, data processing platforms and in-memory databases. This paper presents a new concurrent…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…

The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…

Deep research agents, which synthesize information across diverse sources, are significantly constrained by the sequential nature of reasoning. This bottleneck results in high latency, poor runtime adaptability, and inefficient resource…

Tree-like structures, such as blood vessels, often express complexity at very fine scales, requiring high-resolution grids to adequately describe their shape. Such sparse morphology can alternately be represented by locations of centreline…

Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…

We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let $S$ be a set of $n$ points in the plane, where each point $p$ in $S$ is assigned a weight…

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

Web space is the huge repository of data. Everyday lots of new information get added to this web space. The more the information, more is demand for tools to access that information. Answering users' queries about the online information…

Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

Spatial and spectral approaches are two major approaches for image processing tasks such as image classification and object recognition. Among many such algorithms, convolutional neural networks (CNNs) have recently achieved significant…

Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…

Inverted indexes allow to query large databases without needing to search in the database at each query. An important line of research is to construct the most efficient inverted indexes, both in terms of compression ratio and time…

Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer…

Sensor-based time series analysis is an essential task for applications such as activity recognition and brain-computer interface. Recently, features extracted with deep neural networks (DNNs) are shown to be more effective than…