Unassigned distance geometry and the Buckminsterfullerene
Abstract
The Buckminsterfullerene is an inorganic molecule consisting of 60 carbon atoms in the shape of a soccer ball. It was used in [15] to showcase algorithms that find the correct shape of a protein from limited data (length of inter-atomic distances) without any further chemical experiment: in that case, by means of a complicated constructive heuristic based on genetic algorithms. In this paper we show that we can reconstruct the Buckminsterfullerene structure by means of mathematical programming, standard solver software, and little else.
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