%0 Journal Article %1 844.05093 %A Hendrickson, Bruce %D 1995 %J SIAM J. Optim. %K X a data distances; function; interatomic intermolecular molecule; of optimization; penalty ray rigidity; structure %N 4 %P 835-857 %T The molecule problem: Exploiting structure in global optimization. %V 5 %X Discusses the problem of determining the structure of a molecule when some (but not all) of the interatomic distances are known, this can be, for example, from nuclear magnetic resonance data. The concept of rigidity is introduced which is closely related to the complexity of the corresponding graph; and a penalty function that penalizes inconsistencies in the data which are found to occur and produces a most probable result. An algorithm, the ABBIE ``divide and conquer'' algorithm, uses various tricks to reduce the size of the graph corresponding to the intermolecular distances that are known. Various details of the optimization process are related to recent results in graph theory.\par The reviewer notes: The problem is similar to the old one of determining a structure from X ray data. Obviously, systematic graph theoretical studies will help in both problems.

@article{844.05093, abstract = {Discusses the problem of determining the structure of a molecule when some (but not all) of the interatomic distances are known, this can be, for example, from nuclear magnetic resonance data. The concept of rigidity is introduced which is closely related to the complexity of the corresponding graph; and a penalty function that penalizes inconsistencies in the data which are found to occur and produces a most probable result. An algorithm, the ABBIE ``divide and conquer'' algorithm, uses various tricks to reduce the size of the graph corresponding to the intermolecular distances that are known. Various details of the optimization process are related to recent results in graph theory.\par The reviewer notes: The problem is similar to the old one of determining a structure from X ray data. Obviously, systematic graph theoretical studies will help in both problems. }, added-at = {2008-03-02T02:12:02.000+0100}, author = {Hendrickson, Bruce}, biburl = {https://www.bibsonomy.org/bibtex/2c594c22429cc663507654c6665223822/dmartins}, classmath = {*05C99 Graph theory 49M27 Decomposition methods 51K99 Distance geometry}, description = {robotica-bib}, interhash = {6b591d161229a2bf6d9ca58921f1fa35}, intrahash = {c594c22429cc663507654c6665223822}, journal = {SIAM J. Optim.}, keywords = {X a data distances; function; interatomic intermolecular molecule; of optimization; penalty ray rigidity; structure}, language = {English}, number = 4, pages = {835-857}, reviewer = {H.N.V.Temperley (Langport)}, timestamp = {2008-03-02T02:13:04.000+0100}, title = {The molecule problem: Exploiting structure in global optimization.}, volume = 5, year = 1995 }