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Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
Given a graph G=(V, E), a vertex is said to ve-dominate an edge if it is either incident with the edge or adjacent to one of its endpoints. A set of vertices is a ve-dominating set if it ve-dominates every edge of the graph. We introduce…
The problem of automated separation of stars and galaxies on photographic plates is revisited with two goals in mind : First, to separate galaxies from everything else (as opposed to most previous work, in which galaxies were lumped…
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a…
We give necessary and sufficient conditions for a nonexpansive map on a finite dimensional normed space to have a nonempty, bounded set of fixed points. Among other results we show that if $f : V \rightarrow V$ is a nonexpansive map on a…
This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…
Building upon the concepts and mechanisms used for the development in Moving Points Algorithm, we will now explore how non linear decision boundaries can be developed for classification tasks. First we will look at the classification…
Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$, respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ and $B$ are linearly separable. Our algorithm exploits the…
The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under…
The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…
A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this paper, we consider the…
Let $\Pi_q$ be an arbitrary finite projective plane of order $q$. A subset $S$ of its points is called saturating if any point outside $S$ is collinear with a pair of points from $S$. Applying probabilistic tools we improve the upper bound…
The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…
We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
Given a set $S$ of $n$ static points and a free point $p$ in the Euclidean plane, we study a new variation of the minimum enclosing circle problem, in which a dynamic weight that equals to the reciprocal of the distance from the free point…
This paper proposes a novel point-cloud-based place recognition system that adopts a deep learning approach for feature extraction. By using a convolutional neural network pre-trained on color images to extract features from a range image…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not…