Related papers: A Geometry-Grounded Data Perimeter in Azure
This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete…
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
Hyperparameter tuning is a common practice in the application of machine learning but is a typically ignored aspect in the literature on privacy-preserving machine learning due to its negative effect on the overall privacy parameter. In…
Companies like Amazon and UPS are heavily invested in last-mile delivery problems. Optimizing last-delivery operations not only creates tremendous cost savings for these companies but also generate broader societal and environmental…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
We consider the problem of estimating the perimeter of a smooth domain in the plane based on a sample from the uniform distribution over the domain. We study the performance of the estimator defined as the perimeter of the alpha-shape of…
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization…
We give unconditional parameterized complexity lower bounds on pure dynamic programming algorithms - as modeled by tropical circuits - for connectivity problems such as the Traveling Salesperson Problem. Our lower bounds are higher than the…
This paper presents a learning-based framework for estimating pursuer parameters in turn-rate-limited pursuit-evasion scenarios using sacrificial agents. Each sacrificial agent follows a straight-line trajectory toward an adversary and…
In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. Using this definition we prove: - A bounded-curvature surface embedded spaces TSP admits to a PTAS. -…
Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case where truly subquadratic-time algorithms were given for simple objects such as unit-disks and…
Delay Tolerant Networking (DTN) aims to address a myriad of significant networking challenges that appear in time-varying settings, such as mobile and satellite networks, wherein changes in network topology are frequent and often subject to…
Point cloud registration approaches often fail when the overlap between point clouds is low due to noisy point correspondences. This work introduces a novel cross-attention mechanism tailored for Transformer-based architectures that tackles…
We consider the online versions of two fundamental routing problems, traveling salesman (TSP) and dial-a-ride (DARP), which have a variety of relevant applications in logistics and robotics. The online versions of these problems concern…
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…
In the last years we have witnessed the appearance of a variety of strategies to design optimal location privacy-preserving mechanisms, in terms of maximizing the adversary's expected error with respect to the users' whereabouts. In this…
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…