On the Identification of Discretization Orders for Distance Geometry with Intervals

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Abstract

The discretization of instances of the distance geometry problem is possible when some particular assumptions are satisfied. When molecules are concerned, such assumptions strongly depend on the order in which the atoms of the molecule are considered. When the chemical composition of the molecule is known, as it is the case for the proteins, a general order can be identified for an entire class of instances. However, when this information is not available, ad-hoc orders need to be found for every considered instance. In this paper, the problem of finding discretization orders for distance geometry problems with intervals is formalized, and an algorithm for its solution is presented.