A Theory of Network Localization
James Aspnes,Tolga Eren,David K. Goldenberg,A.S. Morse,Walter Whiteley,Yang Yang,Brian D. O. Anderson,Peter N. Belhumeur +7 more
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TLDR
This paper constructs grounded graphs to model network localization and applies graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks, and further study the computational complexity of network localization.Abstract:
In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomlyread more
Figures
Fig. 1. Two first-order rigid formations with the same graph and the same distance values. ![Fig. 2. An example from [24] showing a rigid triconnected graph with two realizations. If edge (a, a′) is removed, triangle a′b′c′ swings along a path until the distance (a, a′) is the same as it originally was.](/figures/fig-2-an-example-from-24-showing-a-rigid-triconnected-graph-35h5b71h.png)
Fig. 2. An example from [24] showing a rigid triconnected graph with two realizations. If edge (a, a′) is removed, triangle a′b′c′ swings along a path until the distance (a, a′) is the same as it originally was. 
TABLE I LOCALIZATION IN VARIOUS BEACON PLACEMENT SCHEMES. 
Fig. 4. Wheel graph W6. 
Fig. 10. Required steps for algorithm completion. 
Fig. 5. Probability that Gn(r) is k-connected. Dotted line represents the probability that Gn(r) is globally rigid.
![Fig. 2. An example from [24] showing a rigid triconnected graph with two realizations. If edge (a, a′) is removed, triangle a′b′c′ swings along a path until the distance (a, a′) is the same as it originally was.](/figures/fig-2-an-example-from-24-showing-a-rigid-triconnected-graph-35h5b71h.webp)
Citations
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References
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