Challenges for extending Discretizable Molecular Distance Geometry to interval data
نویسندگان
چکیده
The existence of an embedding in R satisfying a set of exact distances can be verified by the Cayley-Menger conditions [2]. In the MDGP, a set of distances is embeddable if and only if all Cayley-Menger determinants of 3 and 4 points have the correct sign(corresponding to the triangular and tetrangular inequalities) and the ones of 5 and 6 points vanish. Another way to verify the embeddability of a set of distances in a generic K-dimensional space is answering whether a partial distance matrix (Dij = d 2 ij), with missing entries, can be completed to a Euclidean distance matrix D. If so, the Cartesian coordinates can be obtained, in polynomial time, by factoring K†(D) = XX, where K†(D) is a linear transformation of D and X is a K ×N matrix whose columns are the coordinates of the N points [3].
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