TY - JOUR
T1 - Packing plane spanning graphs with short edges in complete geometric graphs
AU - Aichholzer, Oswin
AU - Hackl, Thomas
AU - Korman, Matias
AU - Pilz, Alexander
AU - van Renssen, André
AU - Roeloffzen, Marcel
AU - Rote, Günter
AU - Vogtenhuber, Birgit
N1 - Funding Information:
This research was initiated during the 10th European Research Week on Geometric Graphs (GGWeek 2013), Illgau, Switzerland. We would like to thank all participants for fruitful discussions. O.A., A.P., and B.V. were partially supported by the ESF EUROCORES programme EuroGIGA - ComPoSe, Austrian Science Fund (FWF): I 648-N18 . T.H. was supported by the Austrian Science Fund (FWF): P23629-N18 ‘Combinatorial Problems on Geometric Graphs’. M.K. was supported in part by the ELC project ( MEXT KAKENHI No. 17K12635 ) and National Science Foundation (US) award CCF-1423615 . A.P. is supported by an Erwin Schrödinger fellowship, Austrian Science Fund (FWF): J-3847-N35 . A.v.R. and M.R. were supported by JST ERATO Grant Number JPMJER1201 , Japan.
Funding Information:
This research was initiated during the 10th European Research Week on Geometric Graphs (GGWeek 2013), Illgau, Switzerland. We would like to thank all participants for fruitful discussions. O.A. A.P. and B.V. were partially supported by the ESF EUROCORES programme EuroGIGA - ComPoSe, Austrian Science Fund (FWF): I 648-N18. T.H. was supported by the Austrian Science Fund (FWF): P23629-N18 ‘Combinatorial Problems on Geometric Graphs’. M.K. was supported in part by the ELC project (MEXT KAKENHI No. 17K12635)and National Science Foundation (US)award CCF-1423615. A.P. is supported by an Erwin Schrödinger fellowship, Austrian Science Fund (FWF): J-3847-N35. A.v.R. and M.R. were supported by JST ERATO Grant Number JPMJER1201, Japan.
Publisher Copyright:
© 2019
PY - 2019/9
Y1 - 2019/9
N2 - Given a set of points in the plane, we want to establish a connected spanning graph between these points, called connection network, that consists of several disjoint layers. Motivated by sensor networks, our goal is that each layer is connected, spanning, and plane. No edge in this connection network is too long in comparison to the length needed to obtain a spanning tree. We consider two different approaches. First we show an almost optimal centralized approach to extract two layers. Then we consider a distributed model in which each point can compute its adjacencies using only information about vertices at most a predefined distance away. We show a constant factor approximation with respect to the length of the longest edge in the graphs. In both cases the obtained layers are plane.
AB - Given a set of points in the plane, we want to establish a connected spanning graph between these points, called connection network, that consists of several disjoint layers. Motivated by sensor networks, our goal is that each layer is connected, spanning, and plane. No edge in this connection network is too long in comparison to the length needed to obtain a spanning tree. We consider two different approaches. First we show an almost optimal centralized approach to extract two layers. Then we consider a distributed model in which each point can compute its adjacencies using only information about vertices at most a predefined distance away. We show a constant factor approximation with respect to the length of the longest edge in the graphs. In both cases the obtained layers are plane.
KW - Bottleneck edge
KW - Geometric graphs
KW - Graph packing
KW - Minimum spanning tree
KW - Plane graphs
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U2 - 10.1016/j.comgeo.2019.04.001
DO - 10.1016/j.comgeo.2019.04.001
M3 - Article
AN - SCOPUS:85065057729
VL - 82
SP - 1
EP - 15
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
SN - 0925-7721
ER -