Related papers: Continuous Location under Refraction
We study planar point location in a collection of disjoint fat regions, and investigate the complexity of \emph {local updates}: replacing any region by a different region that is "similar" to the original region. (i.e., the size differs by…
The recent large scale availability of mobility data, which captures individual mobility patterns, poses novel operational problems that are exciting and challenging. Motivated by this, we introduce and study a variant of the…
Modeling place functions from a computational perspective is a prevalent research topic. Trajectory embedding, as a neural-network-backed dimension reduction technology, allows the possibility to put places with similar social functions at…
It has been recently understood that the harmonic measure on the boundary $E = \partial \Omega$ of a domain $\Omega$ in $\mathbb{R}^n$ is absolutely continuous with respect to the Hausdorff measure $\mathcal{H}^{n - 1}$ on $E$ if and only…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
In traditional facility location problems, a set of points is provided, and the objective is to determine the best location for a new facility based on criteria such as minimizing cost, time, and distances between clients and facilities.…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…
We study the extended version of the non-uniform, capacitated facility location problem with multiple fulfilment channels between the facilities and clients, each with their own channel capacities and service cost. Though the problem has…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
The task of "relative placement" is to predict the placement of one object in relation to another, e.g. placing a mug onto a mug rack. Through explicit object-centric geometric reasoning, recent methods for relative placement have made…
The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis…
For Euclidean space ($\ell_2$), there exists the powerful dimension reduction transform of Johnson and Lindenstrauss, with a host of known applications. Here, we consider the problem of dimension reduction for all $\ell_p$ spaces $1 \le p…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image),…
We first describe a reduction from the problem of lower-bounding the number of distinct distances determined by a set $S$ of $s$ points in the plane to an incidence problem between points and a certain class of helices (or parabolas) in…
Consider a finite collection of affine hyperplanes in $\mathbb R^d$. The hyperplanes dissect $\mathbb R^d$ into finitely many polyhedral chambers. For a point $x\in \mathbb R^d$ and a chamber $P$ the metric projection of $x$ onto $P$ is the…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
This research presents a novel method of determining relative bearing and elevation measurements, to a remote signal, that is suitable for implementation on small embedded systems - potentially in a GPS denied environment. This is an…