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Proceedings of the 2004 joint workshop on Foundations of mobile computing, 2004
Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a non-approximability result for the problem of embedding a given unit disk graph ...
Fabian Kuhn +2 more
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Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a non-approximability result for the problem of embedding a given unit disk graph ...
Fabian Kuhn +2 more
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Vertex-Edge Domination in Unit Disk Graphs
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sangram K. Jena, Gautam K. Das
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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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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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Hierarchically specified unit disk graphs
1994We characterize the complexity of several basic optimization problems for unit disk graphs specified hierarchically as in [LW87a, Le88, LW92]. Both PSPACE-hardness results and polynomial time approximations are presented for most of the problems considered.
M. V. Marathe +3 more
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Ad hoc networks beyond unit disk graphs
Wireless Networks, 2003In this paper, we study an algorithmic model for wireless ad hoc and sensor networks that aims to be sufficiently close to reality as to represent practical real-world networks while at the same time being concise enough to promote strong theoretical results.
Kuhn, Fabian +2 more
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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
Ding-Zhu Du, Peng-Jun Wan
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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
Ding-Zhu Du, Peng-Jun Wan
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Liar’s dominating set problem on unit disk graphs
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ramesh K. Jallu, Gautam K. Das
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Planar Hop Spanners for Unit Disk Graphs
2010The simplest model of a wireless network graph is the Unit Disk Graph (UDG): an edge exists in UDG if the Euclidean distance between its endpoints is ≤ 1. The problem of constructing planar spanners of Unit Disk Graphs with respect to the Euclidean distance has received considerable attention from researchers in computational geometry and ad-hoc ...
Catusse, Nicolas +2 more
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Approximate Strong Edge-Colouring of Unit Disk Graphs
2020We 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 +3 more
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Weighted CDS in Unit Disk Graph
2012It 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 ...
Ding-Zhu Du, Peng-Jun Wan
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