The Geodesic Edge Center of a Simple Polygon

The geodesic edge center of a polygon is a point c inside the polygon that minimizes the maximum geodesic distance from c to any edge of the polygon, where geodesic distance is the shortest path distance inside the polygon. We give a linear-time algorithm to find a geodesic edge center of a simple polygon. This improves on the previous O(n log n) time algorithm by Lubiw and Naredla [European Symposium on Algorithms, 2021]. The algorithm builds on an algorithm to find the geodesic vertex center of a simple polygon due to Pollack, Sharir, and Rote [Discrete & Computational Geometry, 1989] and an improvement to linear time by Ahn, Barba, Bose, De Carufel, Korman, and Oh [Discrete & Computational Geometry, 2016]. The geodesic edge center can easily be found from the geodesic farthest-edge Voronoi diagram of the polygon. Finding that Voronoi diagram in linear time is an open question, although the geodesic nearest edge Voronoi diagram (the medial axis) can be found in linear time. As a first step of our geodesic edge center algorithm, we give a linear-time algorithm to find the geodesic farthest-edge Voronoi diagram restricted to the polygon boundary

The Visibility Center of a Simple Polygon

We introduce the visibility center of a set of points inside a polygon - a point c_V such that the maximum geodesic distance from c_V to see any point in the set is minimized. For a simple polygon of n vertices and a set of m points inside it, we give an O((n+m) log (n+m)) time algorithm to find the visibility center. We find the visibility center of all points in a simple polygon in O(n log n) time. Our algorithm reduces the visibility center problem to the problem of finding the geodesic center of a set of half-polygons inside a polygon, which is of independent interest. We give an O((n+k) log (n+k)) time algorithm for this problem, where k is the number of half-polygons

Algorithms for Geometric Facility Location: Centers in a Polygon and Dispersion on a Line

We study three geometric facility location problems in this thesis. First, we consider the dispersion problem in one dimension. We are given an ordered list of (possibly overlapping) intervals on a line. We wish to choose exactly one point from each interval such that their left to right ordering on the line matches the input order. The aim is to choose the points so that the distance between the closest pair of points is maximized, i.e., they must be socially distanced while respecting the order. We give a new linear-time algorithm for this problem that produces a lexicographically optimal solution. We also consider some generalizations of this problem. For the next two problems, the domain of interest is a simple polygon with n vertices. The second problem concerns the visibility center. The convention is to think of a polygon as the top view of a building (or art gallery) where the polygon boundary represents opaque walls. Two points in the domain are visible to each other if the line segment joining them does not intersect the polygon exterior. The distance to visibility from a source point to a target point is the minimum geodesic distance from the source to a point in the polygon visible to the target. The question is: Where should a single guard be located within the polygon to minimize the maximum distance to visibility? For m point sites in the polygon, we give an O((m + n) log (m + n)) time algorithm to determine their visibility center. Finally, we address the problem of locating the geodesic edge center of a simple polygon—a point in the polygon that minimizes the maximum geodesic distance to any edge. For a triangle, this point coincides with its incenter. The geodesic edge center is a generalization of the well-studied geodesic center (a point that minimizes the maximum distance to any vertex). Center problems are closely related to farthest Voronoi diagrams, which are well- studied for point sites in the plane, and less well-studied for line segment sites in the plane. When the domain is a polygon rather than the whole plane, only the case of point sites has been addressed—surprisingly, more general sites (with line segments being the simplest example) have been largely ignored. En route to our solution, we revisit, correct, and generalize (sometimes in a non-trivial manner) existing algorithms and structures tailored to work specifically for point sites. We give an optimal linear-time algorithm for finding the geodesic edge center of a simple polygon

Distant Representatives for Rectangles in the Plane

The input to the distant representatives problem is a set of n objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are axis-aligned rectangles, we give polynomial time constant-factor approximation algorithms for the L?, L?, and L_? distance measures. We also prove lower bounds on the approximation factors that can be achieved in polynomial time (unless P = NP)

Shortest Beer Path Queries in Interval Graphs

Our interest is in paths between pairs of vertices that go through at least one of a subset of the vertices known as beer vertices. Such a path is called a beer path, and the beer distance between two vertices is the length of the shortest beer path. We show that we can represent unweighted interval graphs using 2n log n + O(n) + O(|B|log n) bits where |B| is the number of beer vertices. This data structure answers beer distance queries in O(log^? n) time for any constant ? > 0 and shortest beer path queries in O(log^? n + d) time, where d is the beer distance between the two nodes. We also show that proper interval graphs may be represented using 3n + o(n) bits to support beer distance queries in O(f(n)log n) time for any f(n) ? ?(1) and shortest beer path queries in O(d) time. All of these results also have time-space trade-offs. Lastly we show that the information theoretic lower bound for beer proper interval graphs is very close to the space of our structure, namely log(4+2?3)n - o(n) (or about 2.9 n) bits

Detection of Hyperpartisan news articles using natural language processing techniques

Yellow journalism has increased the spread of hyperpartisan news on the internet. It is very difficult for online news article readers to distinguish hyperpartisan news articles from mainstream news articles. There is a need for an automated model that can detect hyperpartisan news on the internet and tag them as hyperpartisan so that it is very easy for readers to avoid that news. A hyperpartisan news detection article was developed by using three different natural language processing techniques named BERT, ELMo, and Word2vec. This research used the bi-article dataset published at SEMEVAL-2019. The ELMo word embeddings which are trained on a Random forest classifier has got an accuracy of 0.88, which is much better than other state of art models. The BERT and Word2vec models have got the same accuracy of 0.83. This research tried different sentence input lengths to BERT and proved that BERT can extract context from local words. Evidenced from the described ML models, this study will assist the governments, news’ readers, and other political stakeholders to detect any hyperpartisan news, and also helps policy to track, and regulate, misinformation about the political parties and their leaders

Direct Amination of alpha-Hydroxy Amides

A TiCl4-mediated reaction for the direct amination of alpha-hydroxy amides has been developed. This simple, general, additive/base/ligand-free reaction is mediated by economical TiCl4. The reaction runs under mild conditions. This highly efficient C-N bond formation protocol is valid for diverse amines, including primary, secondary and heterocyclic amines, and even a primary amide and indole

Hexafluoroisopropanol-Promoted Metal-Free Allylation of Silyl Enol Ethers with Allylic Alcohols

A metal-free protocol for the reaction of silyl enol ethers with allylic alcohols based on the use of 1,1,1,3,3,3-hexafluoroisopropanol as a promoter able to activate both reactants, is described. This simple and straightforward transformation proceeds smoothly under mild conditions, rendering the corresponding allylated products in generally good yields.Financial support from the University of Alicante (UAUSTI16-03, UAUSTI16-10, VIGROB-173) and the Spanish Ministerio de Economía, Industria y Competitividad (CTQ2015-66624-P) is acknowledged