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Journal Articles Optimization Letters Year : 2012

Discretization Orders for Distance Geometry Problems


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.

Dates and versions

hal-00756941 , version 1 (24-11-2012)



Antonio Mucherino, Carlile Lavor, Lee Jon, John Lee S., Leo Liberti, et al.. Discretization Orders for Distance Geometry Problems. Optimization Letters, 2012, 6 (4), pp.783-796. ⟨10.1007/s11590-011-0302-6⟩. ⟨hal-00756941⟩
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