Related papers: Complete and Sufficient Spatial Domination of Mult…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a…
Priebe et al. (2001) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one dimensional data. In higher dimensions these calculations are extremely difficult due to the…
Spatial understanding is a crucial capability that enables robots to perceive their surroundings, reason about their environment, and interact with it meaningfully. In modern robotics, these capabilities are increasingly provided by…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
In this article we prove a necessary and a sufficient condition for a finite subset of the special linear group to be dominated. These conditions are purely geometric in nature, as they only involve the trace and the eigenvectors of the…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbour with label 2. We study the problem of finding a low-cost…
Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by…
Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of…
Existing computer vision systems can compete with humans in understanding the visible parts of objects, but still fall far short of humans when it comes to depicting the invisible parts of partially occluded objects. Image amodal completion…
We use the domination number of a parametrized random digraph family called proportional-edge proximity catch digraphs (PCDs) for testing multivariate spatial point patterns. This digraph family is based on relative positions of data points…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…
One essential step to realize modern driver assistance technology is the accurate knowledge about the location of static objects in the environment. In this work, we use artificial neural networks to predict the occupation state of a whole…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
A beacon is a point-like object which can be enabled to exert a magnetic pull on other point-like objects in space. Those objects then move towards the beacon in a greedy fashion until they are either stuck at an obstacle or reach the…
Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of…