Related papers: Faster Dynamic Compressed d-ary Relations
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
We present a binary tree that describes the 2-adic valuation of a sequence of coefficients arising from the evaluation of a rational integral.
We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant $D$-dimensional tree-level $n$-point amplitudes with pairs of spinning massive particles using compact exponential…
The ten dimensional heterotic string effective action with graviton, dilaton and antisymmetric tensor fields is dimensionally reduced to two spacetime dimensions. The resulting theory, with some constraints on backgrounds, admits infinite…
A central challenge in scaling up explicit state-space search for large tasks is compactly representing the set of generated states. Tree databases, a data structure from model checking, require constant space per generated state in the…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…
The $k$-d tree is one of the oldest and most widely used data structures for nearest neighbor search. It partitions Euclidean space into axis-aligned rectangular cells. There are two standard ways to find the nearest neighbor to a query in…
Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
A $D>2$ topological string is presented by coupling the $2d$ topological gravity with the twisted version of the $N=2$ superconformal matter with $c=3k/(k-2)$. The latter is shown to admit $k+1$ chiral primary fields from the…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core…
Trajectory-based spatiotemporal entity linking is to match the same moving object in different datasets based on their movement traces. It is a fundamental step to support spatiotemporal data integration and analysis. In this paper, we…
Nearest-neighbor search dominates the asymptotic complexity of sampling-based motion planning algorithms and is often addressed with k-d tree data structures. While it is generally believed that the expected complexity of nearest-neighbor…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
Time series clustering is a challenging task due to the specific nature of the data. Classical approaches do not perform well and need to be adapted either through a new distance measure or a data transformation. In this paper we…
This paper describes the most efficient way to manage operations on ranges of elements within an ordered set. The goal is to improve existing solutions, by optimizing the average-case time complexity and getting rid of heavy multiplicative…