An algorithm for drawing general undirected graphs
Information Processing Letters
Conditions for unique graph realizations
SIAM Journal on Computing
Graph drawing by force-directed placement
Software—Practice & Experience
An algorithm for two-dimensional rigidity percolation: the pebble game
Journal of Computational Physics
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Dynamic fine-grained localization in Ad-Hoc networks of sensors
Proceedings of the 7th annual international conference on Mobile computing and networking
Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid
Journal of Combinatorial Theory Series B
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Timing-sync protocol for sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Time synchronization in wireless sensor networks
Time synchronization in wireless sensor networks
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Low-dimensional embedding with extra information
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Robust distributed network localization with noisy range measurements
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Theory of semidefinite programming for sensor network localization
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Topological hole detection in wireless sensor networks and its applications
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
MAP: medial axis based geometric routing in sensor networks
Proceedings of the 11th annual international conference on Mobile computing and networking
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
Localization in sparse networks using sweeps
Proceedings of the 12th annual international conference on Mobile computing and networking
Boundary recognition in sensor networks by topological methods
Proceedings of the 12th annual international conference on Mobile computing and networking
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Plane Embeddings of Planar Graph Metrics
Discrete & Computational Geometry
Geodesic Delaunay triangulation and witness complex in the plane
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graphical properties of easily localizable sensor networks
Wireless Networks
Publish/subscribe in wireless sensor networks based on data centric storage
Proceedings of the 1st International Workshop on Context-Aware Middleware and Services: affiliated with the 4th International Conference on Communication System Software and Middleware (COMSWARE 2009)
Minimum cost localization problem in wireless sensor networks
Ad Hoc Networks
Efficient approximation of routing holes in wireless sensor networks
Proceedings of the Second Symposium on Information and Communication Technology
ELBAR: efficient load balanced routing scheme for wireless sensor networks with holes
Proceedings of the Third Symposium on Information and Communication Technology
Beyond triangle inequality: Sifting noisy and outlier distance measurements for localization
ACM Transactions on Sensor Networks (TOSN)
Cooperative localization revisited: error bound, scaling, and convergence
Proceedings of the 16th ACM international conference on Modeling, analysis & simulation of wireless and mobile systems
Taxonomy of Fundamental Concepts of Localization in Cyber-Physical and Sensor Networks
Wireless Personal Communications: An International Journal
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We study the problem of localizing a large sensor network having a complex shape, possibly with holes. A major challenge with respect to such networks is to figure out the correct network layout, that is, avoid global flips where a part of the network folds on top of another. Our algorithm first selects landmarks on network boundaries with sufficient density, then constructs the landmark Voronoi diagram and its dual combinatorial Delaunay complex on these landmarks. The key insight is that the combinatorial Delaunay complex is provably globally rigid and has a unique realization in the plane. Thus an embedding of the landmarks by simply gluing the Delaunay triangles properly recovers the faithful network layout. With the landmarks nicely localized, the rest of the nodes can easily localize themselves by trilateration to nearby landmark nodes. This leads to a practical and accurate localization algorithm for large networks using only network connectivity. Simulations on various network topologies show surprisingly good results. In comparison, previous connectivity-based localization algorithms such as multidimensional scaling and rubberband representation generate globally flipped or distorted localization results.