Results 21 to 30 of about 89,804 (156)
Improper Colourings of Unit Disk Graphs
Electronic Notes in Discrete Mathematics, 2005 AbstractMotivated by a satellite communications problem, we consider a generalized coloring problem on unit disk graphs. A coloring is k‐improper if no more than k neighbors of every vertex have the same colour as that assigned to the vertex. The k‐improper chromatic number χk(G) is the least number of colors needed in a k‐improper coloring of a graph ...
Havet, Frédéric +2 more
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Balanced Line Separators of Unit Disk Graphs [PDF]
Computational Geometry, 2017 We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of $n$ unit disks in the plane there exists a line $\ell$ such that $\ell$ intersects at most $O(\sqrt{(m+n)\log{n}})$ disks and each of the halfplanes determined by $\ell$ contains at most $2n/3$ unit disks from the set, where $m$ is the ...
Carmi, Paz +8 more
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Strongly Hyperbolic Unit Disk Graphs
, 2021 The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant.
Bläsius, Thomas +3 more
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Identifying and locating-dominating codes in (random) geometric networks [PDF]
, 2009 International audienceWe model a problem about networks built from wireless devices using identifying and locating-dominating codes in unit disk graphs. It is known that minimising the size of an identifying code is NP-complete even for bipartite graphs.
Müller, Tobias, Sereni, Jean-Sébastien
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On the Complexity of Target Set Selection in Simple Geometric Networks [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual
Michal Dvořák +2 more
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Complexity, 2020 In a wireless ad hoc network, the size of the virtual backbone (VB) is an important factor for measuring the quality of the VB. The smaller the VB is, the less the overhead caused by the VB.
Jiarong Liang +5 more
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Approximating Minimum Independent Dominating Sets in Wireless Networks [PDF]
, 2007 We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth.
Hurink, J.L., Nieberg, T.
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International Journal of Distributed Sensor Networks, 2017 The high attenuation of radio signals in water leaves acoustic waves the most viable communication media for underwater sensor networks. Nevertheless, acoustic communication suffers from significantly high latency because of its low propagation speed ...
Xin Bai, Xiaohui Wei, Sen Bai
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Spanners for geometric intersection graphs with applications
Journal of Computational Geometry, 2012 A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t ...
Martin Fürer +1 more
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Hierarchically specified unit disk graphs
Theoretical Computer Science, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marathe, Madhav V. +3 more
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