Results 131 to 140 of about 124,454 (161)

Hierarchically specified unit disk graphs

1994
We 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, V. Radhakrishnan, H. B. Hunt, S. S. Ravi   +3 more
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Ad hoc networks beyond unit disk graphs

Wireless Networks, 2003
In 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, Wattenhofer, Roger, Zollinger, Aaron   +2 more
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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
Ding-Zhu Du, Peng-Jun Wan
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Liar’s dominating set problem on unit disk graphs

Discrete Applied Mathematics, 2020
zbMATH 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

2010
The 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, Chepoi, Victor, Vaxès, Yann   +2 more
openaire   +4 more sources

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
openaire   +4 more sources

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 ...
Ding-Zhu Du, Peng-Jun Wan
openaire   +1 more source

A novel data structure for unit disk graphs

2005
Doubly connected edge list are used in computational geometry to represent plane graphs. The authors suggest an extension that covers unit-disk graphs too, and use it in a routing algorithm.
Li, J., Liang, X., Selvaraj, Henry, Muthukumar, Venkatesan, Gewali, Laxmi P.   +4 more
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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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Tree covers of unit disk graphs

We study the tree cover problem of the unit disk graph(UDG) metric, which is the shortest path distance metric induced by UDGs. We show that the UDG of a set of n points in the plane has a tree cover of O(1) trees with distortion O(1) in both weighted and unweighted settings.
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