Results 211 to 220 of about 116,078 (220)

On Coloring Unit Disk Graphs

Algorithmica, 1998
In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal-sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark et al.
Albert Gräf, Gerhard Weißenfels, M. Stumpf   +2 more
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Vertex-Edge Domination in Unit Disk Graphs

Discrete Applied Mathematics, 2020
Abstract Let G = ( V , E ) be a simple undirected graph. A set D ⊆ V is called a vertex-edge dominating set of G if for each edge e = u v ∈ E , either u or v is in D or one vertex from their neighbor is in D . Simply, a vertex v ∈ V , vertex-edge dominates every edge u v
Sangram K. Jena, Gautam K. Das
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CDS in Unit Disk Graph

2012
A unit disk is a disk with diameter one. Denote by disk r (o) the disk with center o and radius r. A graph G = (V, E) is called a unit disk graph if it can be embedded into the Euclidean plane such that an edge between two nodes u and v exists if and only if disk0. 5(u) ∩ disk0. 5(v)≠∅, that is, their Euclidean distance d(u, v) ≤ 1. The unit disk graph
Peng-Jun Wan, Ding-Zhu Du
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Bisectored unit disk graphs

Networks, 2004
AbstractUnit disk graphs form a natural model for cellular radio channel assignment problems under the assumption of equally powerful, omnidirectional transmitters located on a uniform, flat plane. Here, we introduce and give motivation for an extension of this model, namely, sectorization at transmitter sites.
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Approximate Strong Edge-Colouring of Unit Disk Graphs

2020
We show that the strong chromatic index of unit disk graphs is efficiently 6-approximable. This improves on 8-approximability as shown by Barrett, Istrate, Kumar, Marathe, Thite, and Thulasidasan [1]. We also show that strong edge-6-colourability is NP-complete for the class of unit disk graphs.
Grelier, Nicolas, de Joannis de Verclos, Rémi, Kang, Ross, Pirot, François   +3 more
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Weighted CDS in Unit Disk Graph

2012
It was open for many years whether MinW-CDS in unit disk graphs has a polynomial-time constant-approximation or not. Ambuhl et al. [2] discovered the first one. Their solution consists of two stages. At the first stage, they construct a dominating set which is a 72-approximation for the minimum-weight dominating set problem in unit disk graphs as ...
Peng-Jun Wan, Ding-Zhu Du
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Distributed Approximation Algorithms in Unit-Disk Graphs

2006
We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number of rounds in the message passing model and the approximation error can be made O(1/logk|G|) where |G| is the order of the graph and k is ...
Andrzej Czygrinow, Michał Hańćkowiak
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Algorithmic aspects of constrained unit disk graphs

1996
Computational problems on graphs often arise in two- or three-dimensional geometric contexts. Such problems include assigning channels to radio transmitters (graph colouring), physically routing traces on a printed circuit board (graph drawing), and modelling molecules.
Heinz Breu, David G. Kirkpatrick
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Distributed Approximations for Packing in Unit-Disk Graphs

2007
We give a distributed approximation algorithm for the vertexpacking problemin unit-disk graphs. Given a graph H, the algorithm finds in a unit-disk graph G a collection of pairwise disjoint copies of H of size which is approximately equal to the packing number of H in G.
Andrzej Czygrinow, Michał Hańćkowiak
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Plane Hop Spanners for Unit Disk Graphs

2019
The unit disk graph (UDG) is a widely employed model for the study of wireless networks. In this model, wireless nodes are represented by points in the plane and there is an edge between two points if and only if their Euclidean distance is at most one.
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