Abstract
In this chapter, we address the question: given a graph, does it have a trilateration order? And if so, is it contiguous? Unlike the DGP, which is not known to be in NP, these order existence problems are both in NP: if a graph is a YES instance, a suitable vertex order can be verified to be correct in polytime, by simply checking that it has enough adjacent predecessors.
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Notes
- 1.
Formally, this is the same as the order called DVOP in [76, 84].
- 2.
This distance is given by the length of the path.
- 3.
In [22], the TOP is called DDGPO and the CTOP is called \(^K\!\)DMDGPO.
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Liberti, L., Lavor, C. (2017). Vertex orders. In: Euclidean Distance Geometry. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-60792-4_6
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DOI: https://doi.org/10.1007/978-3-319-60792-4_6
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