Abstract
Given a weighted undirected graph with and a positive integer K, the distance geometry problem (DGP) asks to find an embedding of G such that for each edge we have. Saxe proved in 1979 that the DGP is NP-complete with K = 1 and doubted the applicability of the Turing machine model to the case with K > 1, because the certificates for YES instances might involve real numbers. This chapter is an account of an unfortunately failed attempt to prove that the DGP is in NP for K = 2. We hope that our failure will motivate further work on the question.
Cite
CITATION STYLE
Beeker, N., Gaubert, S., Glusa, C., & Liberti, L. (2013). Is the distance geometry problem in NP? In Distance Geometry: Theory, Methods, and Applications (Vol. 9781461451280, pp. 85–93). Springer New York. https://doi.org/10.1007/978-1-4614-5128-0_5
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