Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Weighted alpha shapes
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Distributed localization in wireless sensor networks: a quantitative comparison
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Wireless sensor networks
A Scalable Logical Coordinates Framework for Routing in Wireless Sensor Networks
RTSS '04 Proceedings of the 25th IEEE International Real-Time Systems Symposium
On the pitfalls of geographic face routing
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Topological hole detection in wireless sensor networks and its applications
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Characterizing the Impact of Routing Holes on Geographic Routing
ICW '05 Proceedings of the 2005 Systems Communications
Efficient Hop ID based Routing for Sparse Ad Hoc Networks
ICNP '05 Proceedings of the 13TH IEEE International Conference on Network Protocols
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
Beacon vector routing: scalable point-to-point routing in wireless sensornets
NSDI'05 Proceedings of the 2nd conference on Symposium on Networked Systems Design & Implementation - Volume 2
Fault-resilient sensing in wireless sensor networks
Computer Communications
Localised convex hulls to identify boundary nodes in sensor networks
International Journal of Sensor Networks
Fast localized delaunay triangulation
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
UNFOLD: uniform fast on-line boundary detection for dynamic 3D wireless sensor networks
MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
Journal of Network and Computer Applications
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Intuitively, many wireless and sensing applications benefit from knowledge of network boundaries. Many virtual coordinate constructions rely on the furthest set of nodes as beacons. Network edges may also bound routing holes in the network, regions of failure due to environmental effects, or indicate the need for additional deployment. In this paper we solve the edge detection problem locally using a geometric structure called the alpha-shape (@a-shape). For a disc of radius 1/@a, the @a-shape consists of nodes (and joining edges) that sit on the boundary of the discs that contain no other nodes in the network. In the simplest terms a node decides it is on a network boundary by asking the following question: ''Do I sit on the boundary of a disc of radius 1/@a that contains no other nodes in the network?'' We show that using only local communications our algorithm is provably correct. Boundary nodes may further participate to reduce unwanted detail. We show via simulation that our algorithm identifies meaningful boundaries even in networks of low-density and non-uniform distribution.