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Discretization Orders for Distance Geometry Problems

Abstract : Given a weighted, undirected simple graph G = (V,E,d) the Distance Geometry Problem (DGP) consists in determining an embedding x such that for each (i,j) in E ||xi - xj|| = d(i,j) . Although in general the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V. We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed K. We exhibit computational experiments on a set of proteins whose natural atomic order does not satisfy the order requirements, and compare our approach with some available continuous space searches.
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https://hal.inria.fr/hal-00756941
Contributor : Antonio Mucherino <>
Submitted on : Saturday, November 24, 2012 - 1:29:02 PM
Last modification on : Wednesday, May 6, 2020 - 5:44:13 PM

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  • HAL Id : hal-00756941, version 1

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Antonio Mucherino, Carlile Lavor, Lee Jon, John Lee S., Leo Liberti, et al.. Discretization Orders for Distance Geometry Problems. Optimization Letters, Springer Verlag, 2012, 6 (4), pp.783-796. ⟨hal-00756941⟩

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