{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T13:52:01Z","timestamp":1710251521947},"reference-count":34,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2016,1,12]],"date-time":"2016-01-12T00:00:00Z","timestamp":1452556800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Int Trans Operational Res"],"published-print":{"date-parts":[[2016,9]]},"abstract":"Abstract<\/jats:title>The distance geometry problem (DGP) studies whether a simple weighted undirected graph can be embedded in a given space so that the weights of the edges of G<\/jats:italic>, when available, are the same as the distances between pairs of embedded vertices. The DGP can be discretized when some particular assumptions are satisfied, which are strongly dependent on the vertex ordering assigned to G<\/jats:italic>. In this paper, we focus on the problem of identifying optimal partial discretization orders for the DGP. The solutions to this problem are in fact vertex orders that allow the discretization of the DGP. Moreover, these partial orders are optimal in the sense that they optimize, at each rank, a given set of objectives aimed to improve the structure of the search space after the discretization. This ordering problem is tackled from a theoretical point of view, and some practical experiences on sets of artificially generated instances, as well as on real\u2010life instances, are provided.<\/jats:p>","DOI":"10.1111\/itor.12249","type":"journal-article","created":{"date-parts":[[2016,1,13]],"date-time":"2016-01-13T01:35:38Z","timestamp":1452648938000},"page":"947-967","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Optimal partial discretization orders for discretizable distance geometry"],"prefix":"10.1111","volume":"23","author":[{"given":"Douglas S.","family":"Gon\u00e7alves","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Universidade Federal de Santa Catarina Florianopolis Brazil"}]},{"given":"Antonio","family":"Mucherino","sequence":"additional","affiliation":[{"name":"IRISA University of Rennes 1 Rennes France"}]}],"member":"311","published-online":{"date-parts":[[2016,1,12]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1089\/cmb.2012.0089"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5128-0_18"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02098169"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/28.1.235"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1149283.1149286"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-29550-X_2"},{"issue":"23","key":"e_1_2_9_8_1","first-page":"1","article-title":"An algorithm to enumerate all possible protein conformations verifying a set of distance restraints","volume":"16","author":"Cassioli A.","year":"2015","journal-title":"BMC Bioinformatics"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-007-0176-2"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-013-0135-1"},{"key":"e_1_2_9_11_1","volume-title":"Distance Geometry and Molecular Conformation","author":"Crippen G.M.","year":"1988"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11081-008-9072-0"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2089210"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-014-0724-z"},{"key":"e_1_2_9_15_1","first-page":"1","volume-title":"Studies in Computational Intelligence","author":"Gon\u00e7alves D.","year":"2015"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-011-0302-6"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-011-9402-6"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-011-9799-6"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-3995.2007.00622.x"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/120875909"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-3995.2009.00757.x"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.01.020"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5128-0_16"},{"key":"e_1_2_9_24_1","doi-asserted-by":"crossref","unstructured":"Mucherino A. 2013.On the identification of discretization orders for distance geometry with intervals. InNielsen F. Barbaresco F.(eds)Proceedings of Geometric Science of Information (GSI13) Lecture Notes in Computer Science 8085.Paris France pp.231\u2013238.","DOI":"10.1007\/978-3-642-40020-9_24"},{"key":"e_1_2_9_25_1","doi-asserted-by":"crossref","unstructured":"Mucherino A. 2015a.A pseudo de Bruijn graph representation for discretization orders for distance geometry. InOrtu\u00f1o F. Rojas I.(eds)Proceedings of the 3rd International Work\u2010Conference on Bioinformatics and Biomedical Engineering (IWBBIO15) Lecture Notes in Computer Science 9043 Lecture Notes in Bioinformatics series Granada Spain pp.514\u2013523.","DOI":"10.1007\/978-3-319-16483-0_50"},{"key":"e_1_2_9_26_1","doi-asserted-by":"crossref","unstructured":"Mucherino A. 2015b.Optimal discretization orders for distance geometry: a theoretical standpoint. Proceedings of theInternational Conference on Large\u2010Scale Scientific Computations (LSSC15) Lecture Notes in Computer Science 9374 Sozopol Bulgaria.","DOI":"10.1007\/978-3-319-26520-9_25"},{"key":"e_1_2_9_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2015.08.012"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-011-0358-3"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5128-0"},{"key":"e_1_2_9_30_1","unstructured":"Saxe J. 1979.Embeddability of weighted graphs ink\u2010space is strongly NP\u2010hard. Proceedings ofAllerton Conference in Communications Control and Computing Monticello IL pp.480\u2013489."},{"key":"e_1_2_9_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-011-9644-6"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511805967"},{"key":"e_1_2_9_33_1","first-page":"329","volume-title":"Distance Geometry: Theory, Methods and Applications","author":"Voller Z.","year":"2013"},{"key":"e_1_2_9_34_1","doi-asserted-by":"publisher","DOI":"10.1137\/060669395"},{"key":"e_1_2_9_35_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2010.938757"}],"container-title":["International Transactions in Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fitor.12249","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/itor.12249","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T23:35:27Z","timestamp":1694648127000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/itor.12249"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,12]]},"references-count":34,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["10.1111\/itor.12249"],"URL":"https:\/\/doi.org\/10.1111\/itor.12249","archive":["Portico"],"relation":{},"ISSN":["0969-6016","1475-3995"],"issn-type":[{"value":"0969-6016","type":"print"},{"value":"1475-3995","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,12]]},"assertion":[{"value":"2015-07-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-11-24","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-01-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}