Mobile phone data analysis: A spatial exploration toward hotspot detection

M Ghahramani, MC Zhou… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org
The percentage of processed large-scale heterogeneous data is exploding and technology
is the most obvious reason for the big data issue. Nowadays, the results of data expansion …

Proximity graphs: E, δ, Δ, χ and ω

P Bose, V Dujmović, F Hurtado, J Iacono… - International Journal …, 2012 - World Scientific
Graph-theoretic properties of certain proximity graphs defined on planar point sets are
investigated. We first consider some of the most common proximity graphs of the family of …

Quantitative classification of vortical flows based on topological features using graph matching

PS Krueger, M Hahsler, EV Olinick… - … of the Royal …, 2019 - royalsocietypublishing.org
Vortical flow patterns generated by swimming animals or flow separation (eg behind bluff
objects such as cylinders) provide important insight to global flow behaviour such as fluid …

Proximity algorithms

JSB Mitchell - Handbook of Discrete and Computational …, 2017 - taylorfrancis.com
The notion of distance is fundamental to many aspects of computational geometry. A classic
approach to characterize the distance properties of planar (and high-dimensional) point sets …

Efficient algorithms and edge crossing properties of Euclidean minimum weight Laman graphs

Y Higashikawa, N Katoh… - International Journal of …, 2023 - Taylor & Francis
We investigate the Euclidean minimum weight Laman graph on a planar point set P, MLG
(P) for short. Bereg et al.(2016) studied geometric properties of MLG (P) and showed that the …

[HTML][HTML] Higher-order triangular-distance Delaunay graphs: Graph-theoretical properties

A Biniaz, A Maheshwari, M Smid - Computational Geometry, 2015 - Elsevier
We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a
set P of points in general position in the plane. In TD-Delaunay, the convex distance is …

Lower Bounds for the Thickness and the Total Number of Edge Crossings of Euclidean Minimum Weight Laman Graphs and (2, 2)-Tight Graphs

Y KAWAKAMI, S TAKAHASHI, K SETO… - … on Information and …, 2024 - search.ieice.org
We explore the maximum total number of edge crossings and the maximum geometric
thickness of the Euclidean minimum-weight (k, ℓ)-tight graph on a planar point set P. In this …

[HTML][HTML] Matchings in higher-order Gabriel graphs

A Biniaz, A Maheshwari, M Smid - Theoretical Computer Science, 2015 - Elsevier
Given a set P of n points in the plane, the order-k Gabriel graph on P, denoted by k-GG, has
an edge between two points p and q if and only if the closed disk with diameter pq contains …

Improving upper and lower bounds for the total number of edge crossings of euclidean minimum weight Laman graphs

Y Kobayashi, Y Higashikawa, N Katoh - Computing and Combinatorics …, 2021 - Springer
We investigate the total number of edge crossings (ie, the crossing number) of the Euclidean
minimum weight Laman graph MLG (P) MLG (P) on a planar point set P. Bereg et al.(2016) …

Generalized Delaunay triangulations: Graph-theoretic properties and Algorithms

MP Cano Vila - 2020 - repository.library.carleton.ca
This thesis studies different generalizations of Delaunay triangulations, both from a
combinatorial and algorithmic point of view. The Delaunay triangulation of a point set S …