{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:38:48Z","timestamp":1787337528504,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The paper introduces a special case of the Euclidean distance matrix completion problem of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the minimal spanning tree. Two solutions are proposed: one an adaptation of a more general method based on a dissimilarity parameterized formulation and the other an entirely novel method which constructs the point configuration directly through a guided random search. These methods as well as three standard edcmp methods are described and compared experimentally on real and synthetic data. It is found that the constructive method given by the guided random search algorithm clearly outperforms all others considered here. Notably, standard methods including the adaptation force peculiar and generally unwanted geometric structure on the point configurations their completions produce.<\/jats:p>","DOI":"10.1137\/16m1092350","type":"journal-article","created":{"date-parts":[[2018,2,20]],"date-time":"2018-02-20T15:48:08Z","timestamp":1519141688000},"page":"528-550","source":"Crossref","is-referenced-by-count":4,"title":["Euclidean Distance Matrix Completion and Point Configurations from the Minimal Spanning Tree"],"prefix":"10.1137","volume":"28","author":[{"given":"Adam","family":"Rahman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. Wayne","family":"Oldford","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,2,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008655427845"},{"key":"atypb2","first-page":"2","volume":"59","author":"Anderson E.","year":"1935","journal-title":"Bull. Amer. Iris Soc."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1145\/235815.235821"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/0916069"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2015.2398954"},{"key":"atypb6","first-page":"1","volume":"27","author":"Edelsbrunner H.","year":"2010","journal-title":"Tessellations Sci."},{"key":"atypb7","unstructured":"M. Ester, H.P. Kriegel, J. Sander, and X. Xu,\n                      A density-based algorithm for discovering clusters in large spatial databases with noise\n                      , in Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, Portland, OR, AAAI Press, 1996, pp. 226-231."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2011.643888"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1936.tb02137.x"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344722"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1981.10477643"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"J. C. Gower and G. B. Dijksterhuis,\n                      Procrustes Problems\n                      , vol. 30, Oxford University Press, Oxford, 2004.","DOI":"10.1093\/acprof:oso\/9780198510581.001.0001"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.2307\/2346439"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/070688547"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(95)00096-A"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/090759392"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"N. Krislock and H. Wolkowicz,\n                      Euclidean distance matrices and applications\n                      , in Handbook on Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications, M. Anjos and J. Lasserre, eds., vol. 166 of International Series in Operations Research and Management Science, Springer Science & Business Media, New York, 2011, pp. 879-914.","DOI":"10.1007\/978-1-4614-0769-0_30"},{"key":"atypb18","unstructured":"J. Oksanen, F. G. Blanchet, M. Friendly, R. Kindt, P. Legendre, D. McGlinn, P. R. Minchin, R. B. O'Hara, G. L. Simpson, P. Solymos, M. H. H. Stevens, E. Szoecs, and H. Wagner,\n                      Vegan: Community Ecology Package\n                      , R package version 2.4-3 ed., 2017,https:\/\/CRAN.R-project.org\/package=vegan."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2006.08.007"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.2307\/1412159"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s00357-003-0004-6"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2319"},{"key":"atypb23","unstructured":"M. W. Trosset,\n                      Computing distances between convex sets and subsets of the positive semidefinite matrices\n                      , Technical Report 97-3 MS 134, Rice University, Houston, TX, 1997."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008722907820"},{"key":"atypb25","first-page":"157","author":"Wilkinson L.","year":"2005","journal-title":"IEEE Computer Society"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1971.223083"},{"key":"atypb27","unstructured":"C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal,\n                      Lbfgs-b: Fortran subroutines for large-scale bound constrained optimization\n                      , Report NAM-11, Northwestern University, Evanston, IL, 1994."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1092350","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:15:26Z","timestamp":1787336126000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1092350"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1092350"],"URL":"https:\/\/doi.org\/10.1137\/16m1092350","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}