Related papers: A Sweep-plane Algorithm for Calculating the Isolat…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
A bottleneck plane perfect matching of a set of $n$ points in $\mathbb{R}^2$ is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as {\em bottleneck}. The…
We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are…
An efficient algorithm is developed that identifies all independencies implied by the topology of a Bayesian network. Its correctness and maximality stems from the soundness and completeness of d-separation with respect to probability…
The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
Isolation is a concept from the world of clique enumeration that is mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest…
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in…
We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
We revisit the notion of WSPD (i.e., well-separated pairs-decomposition), presenting a new construction of WSPD for any finite metric space, and show that it is asymptotically instance-optimal in size. Next, we describe a new WSPD…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We present a system for the classification of mountain panoramas from user-generated photographs followed by identification and extraction of mountain peaks from those panoramas. We have developed an automatic technique that, given as input…
In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…