Zobrazeno 1 - 10
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pro vyhledávání: '"Mount, David M."'
Autor:
Acharya, Aditya, Mount, David M.
Geometric data sets arising in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies over time due
Externí odkaz:
http://arxiv.org/abs/2409.11779
Autor:
Gezalyan, Auguste, Kim, Soo, Lopez, Carlos, Skora, Daniel, Stefankovic, Zofia, Mount, David M.
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how to adapt
Externí odkaz:
http://arxiv.org/abs/2312.05987
Autor:
Abdelkader, Ahmed, Mount, David M.
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously. In many r
Externí odkaz:
http://arxiv.org/abs/2308.08791
Approximating convex bodies is a fundamental question in geometry and has a wide variety of applications. Given a convex body $K$ of diameter $\Delta$ in $\mathbb{R}^d$ for fixed $d$, the objective is to minimize the number of vertices (alternatively
Externí odkaz:
http://arxiv.org/abs/2306.15648
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a distance func
Externí odkaz:
http://arxiv.org/abs/2306.15621
Autor:
Bumpus, Madeline, Dai, Xufeng Caesar, Gezalyan, Auguste H., Munoz, Sam, Santhoshkumar, Renita, Ye, Songyu, Mount, David M.
The Hilbert metric is a projective metric defined on a convex body which generalizes the Cayley-Klein model of hyperbolic geometry to any convex set. In this paper we analyze Hilbert Voronoi diagrams in the Dynamic setting. In addition we introduce d
Externí odkaz:
http://arxiv.org/abs/2304.02745
Autor:
Arya, Sunil, Mount, David M.
Approximating convex bodies is a fundamental question in geometry and has a wide variety of applications. Consider a convex body $K$ of diameter $\Delta$ in $\textbf{R}^d$ for fixed $d$. The objective is to minimize the number of vertices (alternativ
Externí odkaz:
http://arxiv.org/abs/2303.09586
Coverings of convex bodies have emerged as a central component in the design of efficient solutions to approximation problems involving convex bodies. Intuitively, given a convex body $K$ and $\epsilon> 0$, a covering is a collection of convex bodies
Externí odkaz:
http://arxiv.org/abs/2303.08349
Autor:
Barequet, Gill, Fukuzawa, Shion, Goodrich, Michael T., Mount, David M., Osegueda, Martha C., Ozel, Evrim
Motivated by blockchain technology for supply-chain tracing of ethically sourced diamonds, we study geometric polyhedral point-set pattern matching as minimum-width polyhedral annulus problems under translations and rotations. We provide two $(1 + \v
Externí odkaz:
http://arxiv.org/abs/2208.05597
Autor:
Acharya, Aditya, Mount, David M.
Motivated by the problem of maintaining data structures for a large sets of points that are evolving over the course of time, we consider the problem of maintaining a set of labels assigned to the vertices of a tree, where the locations of these labe
Externí odkaz:
http://arxiv.org/abs/2203.16264