Results 31 to 40 of about 142,780 (319)
QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs [PDF]
, 2018 A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since
Bonnet, E. +4 more
core +6 more sources
Good quality virtual realization of unit disk graphs
Journal of Computational Geometry, 2011 We consider the problem of finding a realization of an n-vertex unit disk graph (UDG) expressed in general form, say, as an adjacency matrix. The problem is to construct an embedding of the graph in low-dimensional Euclidean space so that the ratio of ...
Sriram Pemmaraju, Imran Pirwani
doaj +1 more source
Impact of Locality on Location Aware Unit Disk Graphs
Algorithms, 2008 Due to their importance for studies oi wireless networks, recent years have seen a surge of activity on the design of local algorithms for the solution of a variety of network tasks. We study the behaviour of algorithms with very low localities.
Evangelos Kranakis, Andreas Wiese
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Local Approximation Schemes for Ad Hoc and Sensor Networks [PDF]
, 2005 We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs.
Kuhn, F. +3 more
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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
openaire +3 more sources
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
openaire +3 more sources
On isolating points using unit disks
Journal of Computational Geometry, 2016 Given a set of points in the plane and a set of disks (that we think of as wireless sensors) which separate the points, we consider the problem of selecting a minimum subset of the disks such that any path between any pair of points is intersected by at ...
Matt Gibson +4 more
doaj +1 more source
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
core +3 more sources
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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