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- In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane1. Each vertex in the graph corresponds to a disk, and there is an edge between two vertices if the corresponding disks intersect within a unit distance of each other. Unit disk graphs are used to model broadcast networks and some problems in computational geometry2.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a unit distance of each other.en.wikipedia.org/wiki/Unit_disk_graphUnit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry.asu.elsevierpure.com/en/publications/unit-disk-gra… - People also ask
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See all on WikipediaUnit disk graph - Wikipedia
In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a unit distance of each other. They are … See more
There are several possible definitions of the unit disk graph, equivalent to each other up to a choice of scale factor:
• Unit disk graphs are the graphs formed from a collection of points in the Euclidean plane, with a vertex … See moreEvery induced subgraph of a unit disk graph is also a unit disk graph. An example of a graph that is not a unit disk graph is the star $${\displaystyle K_{1,6}}$$ with … See more
If one is given a collection of unit disks (or their centres) in a space of any fixed dimension, it is possible to construct the corresponding unit … See more
Beginning with the work of Huson & Sen (1995), unit disk graphs have been used in computer science to model the topology of ad hoc wireless … See more
• Barrier resilience, an algorithmic problem of breaking cycles in unit disk graphs
• Indifference graph, a one-dimensional analogue of the unit disk graphs
• Penny graph, the unit disk graphs for which the disks can be tangent but not overlap ( See moreWikipedia text under CC-BY-SA license Unit disk graphs - ScienceDirect
WEBDec 14, 1990 · Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) …
- Author: Brent N. Clark, Brent N. Clark, Charles J. Colbourn, Charles J. Colbourn, David S. Johnson, David S....
- Publish Year: 1991
unit disk graphs - Graph Classes
WEBA unit disk graph is a disk graph with an intersection model consisting of disks of unit size.
Vertex-edge domination in unit disk graphs - ScienceDirect
WEBOct 15, 2022 · A unit disk graph (UDG) is the intersection graph of equal-radii disks in the plane. Given a set S = { d 1 , d 2 , … , d n } of n circular disks in the plane, each having …
Optimization Problems in Unit-Disk Graphs | SpringerLink
WEBIn this chapter, we have surveyed results from literature on classical combinatorial optimization problems such as the maximum clique, maximum independent set, …
WEBModeling ad hoc and sensor networks as a quasi unit disk graph (as opposed to a unit disk graph) has the advantage of being signiflcantly closer to reality, while still being …
Unit disk graphs — Arizona State University
WEBUnit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some …
WEBA graph is a d-dimensional unit ball graph if its vertices are represented by unit-size balls in Rd, and an edge exists between two vertices if and only if the corresponding balls …
[2409.13403] Dynamic parameterized problems on unit disk …
WEBSep 20, 2024 · Dynamic parameterized problems on unit disk graphs. In this paper, we study fundamental parameterized problems such as k -Path/Cycle, Vertex Cover, …
WEBG = (V,E), thus: V = D; {u,v} ∈ E ⇔ disk(u) ∩ disk(v) 6= ∅. G is called a disk graph; it is a unit disk graph when the disk radii are identical. Given a graph the minimum …
WEBNumerous approximation algorithms for unit disk graphs have been proposed in the literature, exhibiting sharp trade-o s between running times and approximation ratios. …
Unit Disk -- from Wolfram MathWorld
WEBAug 22, 2024 · Unit Disk. A disk with radius 1. The (open) unit disk can also be considered to be the region in the complex plane defined by , where denotes the complex modulus. …
Computing Diameter+2 in Truly Subquadratic Time for Unit-Disk …
WEBJan 23, 2024 · In this paper, we show a truly subquadratic algorithm of running time $\tilde{O}(n^{2-1/18})$, for finding the diameter in a unit-disk graph, whose output differs …
Simple heuristics for unit disk graphs - Wiley Online Library
WEBUnit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP‐hard optimization …
CDS in Unit Disk Graph - SpringerLink
WEBJan 1, 2012 · The unit disk graph is a mathematical model for wireless sensor networks when all sensors have the same communication radius. For any node v of a unit disk …
WEBUnit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some …
WEBUnit disk graphs are the intersection graphs of unit radius disks in the Euclidean plane. Deciding whether there exists an embed-ding of a given unit disk graph, i.e. unit …
Unit disk graph recognition is NP-hard - ScienceDirect
WEBJan 1, 1998 · Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper gives a polynomial-time reduction from SATISFIABILITY to the …
What is the exact algorithm to find maximum clique of a given unit …
WEBA unit disk graph is an intersection graph $G = (V,E)$, such that given $n$ disks on the plane with identical radius. Each disk $d_u$ corresponds to a vertex $u \in V$, and there …
Unit Disk Graphs - ScienceDirect
WEBJan 1, 1991 · Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) …
WEBUnit-disk graphs are a classical model of wireless communication networks, and are a central object of study in distributed algorithms (see the survey [22] for an extensive …
[2107.05518] Strongly Hyperbolic Unit Disk Graphs - arXiv.org
WEBJul 12, 2021 · We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to …
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