An alternative approach to distance geometry using L∞ distances

A standard task in distance geometry is to calculate one or more sets of Cartesian coordinates for a set of points that satisfy given geometric constraints, such as bounds on some of the L 2 distances. Using instead L ∞ distances is attractive because distance constraints can be expressed as simple linear bounds on coordinates. Likewise, a given matrix of L ∞ distances can be rather directly converted to coordinates for the points. It can happen that multiple sets of coordinates correspond precisely to the same matrix of L ∞ distances, but the L 2 distances vary only modestly. Practical examples are given of calculating protein conformations from the sorts of distance constraints that one can obtain from nuclear magnetic resonance experiments.