Related papers: A Geometry-Grounded Data Perimeter in Azure
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
We investigate the geometric hitting set problem in the online setup for the range space $\Sigma=({\cal P},{\cal S})$, where the set $\P\subset\mathbb{R}^2$ is a collection of $n$ points and the set $\cal S$ is a family of geometric objects…
Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that…
In response to the Amazon Last-Mile Routing Challenge, Team Permission Denied proposes a hierarchical Travelling Salesman Problem (TSP) optimization with a customized cost matrix. The higher level TSP solves for the zone sequence while the…
Unmanned Aerial Vehicle (UAV) mounted Base Stations (UAV-BSs) provide flexible coverage for temporary hotspot scenarios; however, efficiently optimizing 3D deployment to satisfy heterogeneous user distributions remains a significant…
In real life, providing security for a set of large areas by covering the area with Unmanned Aerial Vehicles (UAVs) is a difficult problem that consist of multiple objectives. These difficulties are even greater if the area coverage must…
A flexible topological representation consisting of a two-layer graph structure built on-board an Unmanned Aerial Vehicle (UAV) by continuously filling the free space of an occupancy map with intersecting spheres is proposed in this…
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…
The delivery of bulk data is an increasingly pressing problem in modern networks. While in some cases these transfers happen in background without specific constraints in terms of delivery times, there are a number of scenarios in which the…
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining…
We consider the classic correlation clustering problem in the hierarchical setting. Given a complete graph $G=(V,E)$ and $\ell$ layers of input information, where the input of each layer consists of a nonnegative weight and a labeling of…
Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
The efficiency and dynamism of Unmanned Aerial Vehicles (UAVs), or drones, present substantial application opportunities in several industries in the last years. Notably, the logistic companies gave close attention to these vehicles…
Recommender system is the most successful commercial technology in the past decade. Technical mammoth such as Temu, TikTok and Amazon utilize the technology to generate enormous revenues each year. Although there have been enough research…
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic…
Data centers have become ubiquitous for today's businesses. From banks to startups, they rely on cloud infrastructure to deploy user applications. In this context, it is vital to provide users with application performance guarantees.…
This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…
The routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant maximum number of…