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ETH-Tight Algorithms for Long Path and Cycle on Unit Disk Graphs
International Symposium on Computational Geometry, 2020We present an algorithm for the extensively studied Long Path and Long Cycle problems on unit disk graphs that runs in time $2^{O(\sqrt{k})}(n+m)$. Under the Exponential Time Hypothesis, Long Path and Long Cycle on unit disk graphs cannot be solved in ...
F. Fomin +4 more
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Algorithmica, 1998
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Gräf, A., Stumpf, M., Weißenfels, G.
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Gräf, A., Stumpf, M., Weißenfels, G.
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Capacitated discrete unit disk cover
Discrete Applied Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pawan K. Mishra +3 more
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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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On the Discrete Unit Disk Cover Problem
International Journal of Computational Geometry & Applications, 2011Given a set [Formula: see text] of n points and a set [Formula: see text] of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in [Formula: see text] is covered by at least one disk in [Formula: see text] or not and (ii) if so, then find a minimum cardinality subset [Formula: see text]
Das, Gautam K. +3 more
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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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Some Asymptotic Properties of the Solutions of Laplace Equations in a Unit Disk
Cybernetics and Systems Analysis, 2023T. V. Zhyhallo, Yu. I. Kharkevych
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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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Asymptotics of invariant metrics in the normal direction and a new characterisation of the unit disk
, 2016We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics.
E. F. Wold
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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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