Packing Short Plane Spanning Trees in Complete Geometric Graphs
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two trees. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. This second approach may create cycles, but maintains planarity.
Geometric Graphs
Graph Packing
Plane Graphs
Minimum Spanning Tree
Bottleneck Edge
9:1-9:12
Regular Paper
Oswin
Aichholzer
Oswin Aichholzer
Thomas
Hackl
Thomas Hackl
Matias
Korman
Matias Korman
Alexander
Pilz
Alexander Pilz
Günter
Rote
Günter Rote
André
van Renssen
André van Renssen
Marcel
Roeloffzen
Marcel Roeloffzen
Birgit
Vogtenhuber
Birgit Vogtenhuber
10.4230/LIPIcs.ISAAC.2016.9
O. Aichholzer, T. Hackl, M. Korman, M. J. van Kreveld, M. Löffler, A. Pilz, B. Speckmann, and E. Welzl. Packing plane spanning trees and paths in complete geometric graphs. In Proc. Canadian Conference on Computational Geometry (CCCG), pages 233-238, 2014.
P. Bose, P. Morin, I. Stojmenovic, and J. Urrutia. Routing with guaranteed delivery in ad hoc wireless networks. Wireless Networks, 7(6):609-616, 2001.
D. Dor and M. Tarsi. Graph decomposition is NP-complete: A complete proof of Holyer’s conjecture. SIAM Journal on Computing, 26(4):1166-1187, 1997.
M. Fussen, R. Wattenhofer, and A. Zollinger. Interference arises at the receiver. In Proc. International Conference on Wireless Networks, Communications, and Mobile Computing (WIRELESSCOM), pages 427-432, 2005.
A. García. Personal Communication, 2015.
M. Korman. Minimizing interference in ad-hoc networks with bounded communication radius. Information Processing Letters, 112(19):748-752, 2012.
E. Kranakis, H. Singh, and J. Urrutia. Compass routing on geometric networks. In Proc. Canadian Conference on Computational Geometry (CCCG), pages 51-54, 1999.
M. Priesler and M. Tarsi. Multigraph decomposition into stars and into multistars. Discrete Mathematics, 296(2-3):235-244, 2005.
M. Tarsi. Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs. Journal of Combinatorial Theory, Series A, 34(1):60-70, 1983.
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