Related papers: p-Adic scaled space filling curve indices for high…

We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…

Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This…

We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…

Numerical data structures for positive dimensional solution sets of polynomial systems are sets of generic points cut out by random planes of complimentary dimension. We may represent the linear spaces defined by those planes either by…

A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of…

Traditional indexing techniques commonly employed in da\-ta\-ba\-se systems perform poorly on multidimensional array scientific data. Bitmap indices are widely used in commercial databases for processing complex queries, due to their…

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how…

This paper introduces a new way of generalizing Hilbert's two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d' < d, the d-dimensional curve…

Deep learning has become the standard approach for most machine learning tasks. While its impact is undeniable, interpreting the predictions of deep learning models from a human perspective remains a challenge. In contrast to model…

We design the first learned index that solves the dictionary problem with time and space complexity provably better than classic data structures for hierarchical memories, such as B-trees, and modern learned indexes. We call our solution…

Index structures are important for efficient data access, which have been widely used to improve the performance in many in-memory systems. Due to high in-memory overheads, traditional index structures become difficult to process the…

In most practical applications of image retrieval, high-dimensional feature vectors are required, but current multi-dimensional indexing structures lose their efficiency with growth of dimensions. Our goal is to propose a divisive…

We examine space-filling curves, which are surjective continuous maps from $[0,1]$ to some higher-dimensional space, usually the unit square $[0,1]^2$. In particular, we define Peano's curve and Lebesgue's curve, and state some of their…

This paper addresses the problem of exploring a region using the Hilbert's space-filling curve in the presence of obstacles. No prior knowledge of the region being explored is assumed. An online algorithm is proposed which can implement…

The recent introduction of learned indexes has shaken the foundations of the decades-old field of indexing data structures. Combining, or even replacing, classic design elements such as B-tree nodes with machine learning models has proven…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

Space-filling curves (SFCs) are used in high performance computing to distribute a computational domain or its mesh, respectively, amongst different compute units, i.e.~cores or nodes or accelerators. The part of the domain allocated to…

Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enabled devices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and…

In this paper, we develop an algorithm for computing Coleman--Gross (and hence Nekov\'a\v{r}) $p$-adic heights on hyperelliptic curves over number fields with arbitrary reduction type above $p$. This height is defined as a sum of local…

Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity…