Related papers: The geodesic edge center of a simple polygon
The topological (resp. geodesic) complexity of a topological (resp. metric) space is roughly the smallest number of continuous rules required to choose paths (resp. shortest paths) between any points of the space. We prove that the geodesic…
Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface.…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set $S$ of point sites in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a…
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We…
Let $\mathcal{P}$ be a simple polygon with $m$ vertices and let $P$ be a set of $n$ points inside $\mathcal{P}$. We prove that there exists, for any $\varepsilon>0$, a set $\mathcal{C} \subset P$ of size $O(1/\varepsilon^2)$ such that the…
In this paper, we present efficient algorithms for the single-source shortest path problem in weighted disk graphs. A disk graph is the intersection graph of a family of disks in the plane. Here, the weight of an edge is defined as the…
This paper presents the first polynomial time algorithm to compute geodesics in a CAT(0) cubical complex in general dimension. The algorithm is a simple iterative method to update breakpoints of a path joining two points using Miller, Owen…
We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$…
A monitoring edge-geodetic set (or meg-set for short) of a graph is a set of vertices $M$ such that if any edge is removed, then the distance between some two vertices of $M$ increases. This notion was introduced by Foucaud et al. in 2023…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed…
Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a…
A monotone cylindrical graph is a topological graph drawn on an open cylinder with an infinite vertical axis satisfying the condition that every vertical line intersects every edge at most once. It is called simple if any pair of its edges…
The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Omega(n^2) time,…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
A geometric $t$-spanner for a set $S$ of $n$ point sites is an edge-weighted graph for which the (weighted) distance between any two sites $p,q \in S$ is at most $t$ times the original distance between $p$ and~$q$. We study geometric…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
Motivated by the $k$-center problem in location analysis, we consider the \emph{polygon burning} (PB) problem: Given a polygonal domain $P$ with $h$ holes and $n$ vertices, find a set $S$ of $k$ vertices of $P$ that minimizes the maximum…
The median of a set of vertices $P$ of a graph $G$ is the set of all vertices $x$ of $G$ minimizing the sum of distances from $x$ to all vertices of $P$. In this paper, we present a linear time algorithm to compute medians in median graphs,…