Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
A lower bound on the distortion of embedding planar metrics into Euclidean space
Proceedings of the eighteenth annual symposium on Computational geometry
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Deterministic boundary recognition and topology extraction for large sensor networks
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Hole detection or: "how much geometry hides in connectivity?"
Proceedings of the twenty-second annual symposium on Computational geometry
Boundary recognition in sensor networks by topological methods
Proceedings of the 12th annual international conference on Mobile computing and networking
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
International Journal of Robotics Research
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Distributed computation of virtual coordinates
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On the Locality of Extracting a 2-Manifold in
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Segmenting a sensor field: Algorithms and applications in network design
ACM Transactions on Sensor Networks (TOSN)
How much geometry it takes to reconstruct a 2-manifold in R3
Journal of Experimental Algorithmics (JEA)
Greedy routing with guaranteed delivery using Ricci flows
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Connectivity-based localization of large-scale sensor networks with complex shape
ACM Transactions on Sensor Networks (TOSN)
Covering space for in-network sensor data storage
Proceedings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks
Resilient routing for sensor networks using hyperbolic embedding of universal covering space
INFOCOM'10 Proceedings of the 29th conference on Information communications
Differential forms for target tracking and aggregate queries in distributed networks
Proceedings of the sixteenth annual international conference on Mobile computing and networking
Distributed computation of virtual coordinates for greedy routing in sensor networks
Discrete Applied Mathematics
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
Differential forms for target tracking and aggregate queries in distributed networks
IEEE/ACM Transactions on Networking (TON)
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Wireless sensor networks typically consist of small, very simple network nodes without any positioning device like GPS. After an initialization phase, the nodes know with whom they can talk directly, but have no idea about their relative geographic locations. We examine how much geometry information is nevertheless hidden in the communication graph of the network: Assuming that the connectivity is determined by the well-known unit-disk graph model, we show that using a very simple distributed algorithm we can identify a large, provably planar subgraph of the communication graph that faithfully reflects the topology of the network. This planar subgraph can then be embedded using a simple distributed rubber-banding procedure, finally obtaining virtual coordinates for the nodes of the subgraph which can be instrumented for various protocols based on geographic location information. That is, there is enough geometry information hidden in the connectivity structure not only to identify topological features like network holes (as it was also exhibited in the predecessor paper [7]) but even enough information to compute a sketch of the network layout. Our simulation results indicate that the algorithm works very well even for very sparse network deployments and produces network sketches that come close to the original layout.