Related papers: Incremental Voronoi Diagrams
Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…
We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over $\Omega(n)$ operations, is $O(\log^2 n)$. Via SPQR-trees, we give a…
In the Hausdorff Voronoi diagram of a family of \emph{clusters of points} in the plane, the distance between a point $t$ and a cluster $P$ is measured as the maximum distance between $t$ and any point in $P$, and the diagram is defined in a…
This paper applies the randomized incremental construction (RIC) framework to computing the Hausdorff Voronoi diagram of a family of k clusters of points in the plane. The total number of points is n. The diagram is a generalization of…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi…
Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…
We introduce the inverse Voronoi diagram problem in graphs: given a graph $G$ with positive edge-lengths and a collection $\mathbb{U}$ of subsets of vertices of $V(G)$, decide whether $\mathbb{U}$ is a Voronoi diagram in $G$ with respect to…
We study the point location problem in incremental (possibly disconnected) planar subdivisions, that is, dynamic subdivisions allowing insertions of edges and vertices only. Specifically, we present an $O(n\log n)$-space data structure for…
We investigate the extremal properties of saturated partial plane embeddings of maximal planar graphs. For a planar graph $G$, the plane-saturation number $\mathrm{sat}_{\mathcal{P}}(G)$ denotes the minimum number of edges in a plane…
We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in…
Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…
We address the problem of replicating a Voronoi diagram $V(S)$ of a planar point set $S$ by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in…
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design.…
In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams --- generalized Voronoi diagrams with…
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
Given a dynamic digraph $G = (V,E)$ undergoing edge deletions and given $s\in V$ and $\epsilon>0$, we consider the problem of maintaining $(1+\epsilon)$-approximate shortest path distances from $s$ to all vertices in $G$ over the sequence…
Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…