Discretization vertex orders in distance geometry
نویسندگان
چکیده
منابع مشابه
Discretization vertex orders in distance geometry
When a weighted graph is an instance of the Distance Geometry Problem (DGP), certain types of vertex orders (called discretization orders) allow the use of a very efficient, precise and robust discrete search algorithm (called Branch-and-Prune). Accordingly, finding such orders is critically important in order to solve DGPs in practice. We discuss three types of discretization orders, the compl...
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The Distance Geometry Problem (DGP) asks whether a simple weighted undirected graph G = (V,E, d) can be embedded in aK-dimensional space [6]. In the applications,K is generally known a priori : one of the most interesting DGP applications is in biology and concerns molecular conformations, where K = 3. In such a case, G is defined so that vertices v ∈ V represent atoms of a molecule, and some p...
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Given a weighted, undirected simple graph G = (V,E, d) (where d : E → R+), the Distance Geometry Problem (DGP) is to determine an embedding x : V → R K such that ∀{i, j} ∈ E ‖xi − xj‖ = dij . 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 form...
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Distance geometry consists of finding an embedding of a weighted undirected graph inR. Since some years, we are workingonsuitable discretizations for this problem. Because of the discretization, the search domain is reduced froma continuous to a discrete set which has the structure of a tree. Based on this combinatorial structure, we developed an efficient branch-and-prune (BP) algorithm for th...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.08.035