{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:26:40Z","timestamp":1775136400659,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801307"],"award-info":[{"award-number":["11801307"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021MA009"],"award-info":[{"award-number":["ZR2021MA009"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s00186-025-00909-z","type":"journal-article","created":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T14:07:33Z","timestamp":1761228453000},"page":"325-358","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic spanning tree problems with incomplete edge weight information"],"prefix":"10.1007","volume":"102","author":[{"given":"Deguo","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,23]]},"reference":[{"key":"909_CR1","volume-title":"Network Flows: Theory, Algorithms, and Applications","author":"RK Ahuja","year":"1993","unstructured":"Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall Inc, USA"},{"issue":"1","key":"909_CR2","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1287\/mnsc.2022.4352","volume":"69","author":"D Bertsimas","year":"2023","unstructured":"Bertsimas D, Shtern S, Sturt B (2023) A data-driven approach to multistage stochastic linear optimization. Manage Sci 69(1):51\u201374. https:\/\/doi.org\/10.1287\/mnsc.2022.4352","journal-title":"Manage Sci"},{"key":"909_CR3","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/978-3-642-17517-6_38","volume-title":"Algorithms and computation","author":"I Bomze","year":"2010","unstructured":"Bomze I, Chimani M, J\u00fcnger M, Ljubi\u0107 I, Mutzel P, Zey B (2010) Solving two-stage stochastic steiner tree problems by two-stage branch-and-cut. In: Cheong O, Chwa K-Y, Park K (eds) Algorithms and computation. Springer, Berlin, Heidelberg, pp 427\u2013439"},{"issue":"3","key":"909_CR4","first-page":"37","volume":"III","author":"O Bor\u016dvka","year":"1926","unstructured":"Bor\u016dvka O (1926) O jist\u00e9m probl\u00e9mu minim\u00e1ln\u00edm. Pr\u00e1ce Moravsk\u00e9 p\u0159\u00edrodov\u011bdeck\u00e9 spole\u010dnosti sv III(3):37\u201358","journal-title":"Pr\u00e1ce Moravsk\u00e9 p\u0159\u00edrodov\u011bdeck\u00e9 spole\u010dnosti sv"},{"key":"909_CR5","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1007\/s11425-015-5095-0","volume":"59","author":"Z Chen","year":"2016","unstructured":"Chen Z (2016) Strong laws of large numbers for sub-linear expectations. Sci China Math 59:945\u2013954. https:\/\/doi.org\/10.1007\/s11425-015-5095-0","journal-title":"Sci China Math"},{"key":"909_CR6","doi-asserted-by":"publisher","first-page":"105645","DOI":"10.1016\/j.jet.2023.105645","volume":"209","author":"Z Chen","year":"2023","unstructured":"Chen Z, Epstein LG, Zhang G (2023) A central limit theorem, loss aversion and multi-armed bandits. J Econ Theory 209:105645. https:\/\/doi.org\/10.1016\/j.jet.2023.105645","journal-title":"J Econ Theory"},{"issue":"3","key":"909_CR7","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.eswa.2006.06.020","volume":"33","author":"T-C Chiang","year":"2007","unstructured":"Chiang T-C, Liu C-H, Huang Y-M (2007) A near-optimal multicast scheme for mobile ad hoc networks using a hybrid genetic algorithm. Expert Syst Appl 33(3):734\u2013742. https:\/\/doi.org\/10.1016\/j.eswa.2006.06.020","journal-title":"Expert Syst Appl"},{"key":"909_CR8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s11118-010-9185-x","volume":"34","author":"L Denis","year":"2011","unstructured":"Denis L, Hu M, Peng S (2011) Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal 34:139\u2013161. https:\/\/doi.org\/10.1007\/s11118-010-9185-x","journal-title":"Potential Anal"},{"issue":"7","key":"909_CR9","doi-asserted-by":"publisher","first-page":"1740","DOI":"10.1093\/rfs\/hht018","volume":"26","author":"LG Epstein","year":"2013","unstructured":"Epstein LG, Ji S (2013) Ambiguous volatility and asset pricing in continuous time. Rev Finan Stud 26(7):1740\u20131786. https:\/\/doi.org\/10.1093\/rfs\/hht018","journal-title":"Rev Finan Stud"},{"issue":"3","key":"909_CR10","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1016\/j.amc.2004.06.051","volume":"164","author":"J Gao","year":"2005","unstructured":"Gao J, Lu M (2005) Fuzzy quadratic minimum spanning tree problem. Appl Math Comput 164(3):773\u2013788. https:\/\/doi.org\/10.1016\/j.amc.2004.06.051","journal-title":"Appl Math Comput"},{"issue":"2","key":"909_CR11","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1002\/net.3230010203","volume":"1","author":"SL Hakimi","year":"1971","unstructured":"Hakimi SL (1971) Steiner\u2019s problem in graphs and its implications. Networks 1(2):113\u2013133. https:\/\/doi.org\/10.1002\/net.3230010203","journal-title":"Networks"},{"issue":"2","key":"909_CR12","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1137\/15M1037639","volume":"54","author":"M Hu","year":"2016","unstructured":"Hu M, Ji S (2016) Stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity. SIAM J Control Optim 54(2):918\u2013945. https:\/\/doi.org\/10.1137\/15M1037639","journal-title":"SIAM J Control Optim"},{"issue":"2","key":"909_CR13","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1016\/j.spa.2013.10.009","volume":"124","author":"M Hu","year":"2014","unstructured":"Hu M, Ji S, Peng S, Song Y (2014) Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion. Stoch Process Appl 124(2):1170\u20131195. https:\/\/doi.org\/10.1016\/j.spa.2013.10.009","journal-title":"Stoch Process Appl"},{"issue":"3","key":"909_CR14","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1002\/net.3230130311","volume":"13","author":"H Ishii","year":"1983","unstructured":"Ishii H, Nishida T (1983) Stochastic bottleneck spanning tree problem. Networks 13(3):443\u2013449. https:\/\/doi.org\/10.1002\/net.3230130311","journal-title":"Networks"},{"key":"909_CR15","doi-asserted-by":"publisher","unstructured":"Ishii H, Shiode S, Nishida T, Namasuya Y (1981) Stochastic spanning tree problem. Discret Appl Math 3(4):263\u2013273. https:\/\/doi.org\/10.1016\/0166-218X(81)90004-4. Special Copy","DOI":"10.1016\/0166-218X(81)90004-4"},{"key":"909_CR16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.15807\/jorsj.39.247","volume":"39","author":"T Itoh","year":"1996","unstructured":"Itoh T, Ishii H (1996) An approach based on necessity measure to the fuzzy spanning tree problems. J Op Res Soc Japan 39:247\u2013257. https:\/\/doi.org\/10.15807\/jorsj.39.247","journal-title":"J Op Res Soc Japan"},{"issue":"1","key":"909_CR17","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1090\/s0002-9939-1956-0078686-7","volume":"7","author":"JB Kruskal","year":"1956","unstructured":"Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7(1):48\u201350. https:\/\/doi.org\/10.1090\/s0002-9939-1956-0078686-7","journal-title":"Proc Am Math Soc"},{"issue":"3","key":"909_CR18","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10589-017-9966-x","volume":"69","author":"M Leitner","year":"2018","unstructured":"Leitner M, Ljubi\u0107 I, Luipersbeck M, Sinnl M (2018) Decomposition methods for the two-stage stochastic Steiner tree problem. Comput Optim Appl 69(3):713\u2013752","journal-title":"Comput Optim Appl"},{"key":"909_CR19","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1007\/s10957-019-01546-3","volume":"183","author":"H Li","year":"2019","unstructured":"Li H, Wang F (2019) Stochastic optimal control problem with obstacle constraints in sublinear expectation framework. J Optim Theory Appl 183:422\u2013439. https:\/\/doi.org\/10.1007\/s10957-019-01546-3","journal-title":"J Optim Theory Appl"},{"key":"909_CR20","volume-title":"Uncertainty Theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertainty Theory, 2nd edn. Springer, Berlin, Germany","edition":"2"},{"key":"909_CR21","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/B978-044482537-7\/50016-4","volume-title":"Handbook of Computational Geometry","author":"JSB Mitchell","year":"2000","unstructured":"Mitchell JSB (2000) Chapter 15 - geometric shortest paths and network optimization. In: Sack J-R, Urrutia J (eds) Handbook of Computational Geometry. North-Holland, Amsterdam, pp 633\u2013701. https:\/\/doi.org\/10.1016\/B978-044482537-7\/50016-4"},{"issue":"4","key":"909_CR22","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/0305-0548(80)90022-2","volume":"7","author":"SC Narula","year":"1980","unstructured":"Narula SC, Ho CA (1980) Degree-constrained minimum spanning tree. Comput Op Res 7(4):239\u2013249. https:\/\/doi.org\/10.1016\/0305-0548(80)90022-2","journal-title":"Comput Op Res"},{"key":"909_CR24","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/978-3-540-70847-6_25","volume-title":"Stochastic Analysis and Applications","author":"S Peng","year":"2007","unstructured":"Peng S (2007) G-expectation, g-Brownian motion and related stochastic calculus of it\u00f4 type. In: Benth FE, Di Nunno G, Lindstr\u00f8m T, \u00d8ksendal B, Zhang T (eds) Stochastic Analysis and Applications. Springer, Berlin, Heidelberg, pp 541\u2013567. https:\/\/doi.org\/10.1007\/978-3-540-70847-6_25"},{"issue":"12","key":"909_CR25","doi-asserted-by":"publisher","first-page":"2223","DOI":"10.1016\/j.spa.2007.10.015","volume":"118","author":"S Peng","year":"2008","unstructured":"Peng S (2008a) Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stoch Process Appl 118(12):2223\u20132253. https:\/\/doi.org\/10.1016\/j.spa.2007.10.015","journal-title":"Stoch Process Appl"},{"key":"909_CR26","doi-asserted-by":"publisher","unstructured":"Peng S (2008b) A new central limit theorem under sublinear expectations. https:\/\/doi.org\/10.48550\/arXiv.0803.2656","DOI":"10.48550\/arXiv.0803.2656"},{"issue":"7","key":"909_CR27","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1007\/s11425-009-0121-8","volume":"52","author":"S Peng","year":"2009","unstructured":"Peng S (2009) Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci China, Ser A Math 52(7):1391\u20131411. https:\/\/doi.org\/10.1007\/s11425-009-0121-8","journal-title":"Sci China, Ser A Math"},{"key":"909_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-59903-7","volume-title":"Nonlinear expectations and stochastic calculus under uncertainty: with robust CLT and G-Brownian motion","author":"S Peng","year":"2019","unstructured":"Peng S (2019) Nonlinear expectations and stochastic calculus under uncertainty: with robust CLT and G-Brownian motion. Springer, Berlin, Germany"},{"key":"909_CR23","unstructured":"Peng J, Li S (2011) Spanning tree problem of uncertain network. In: Proceedings of the 3rd International Conference on Computer Design and Applications, Xi\u2019an, China"},{"key":"909_CR29","doi-asserted-by":"publisher","first-page":"108623","DOI":"10.1016\/j.spl.2019.108623","volume":"156","author":"S Peng","year":"2020","unstructured":"Peng S, Zhou Q (2020) A hypothesis-testing perspective on the G-normal distribution theory. Stat Prob Lett 156:108623. https:\/\/doi.org\/10.1016\/j.spl.2019.108623","journal-title":"Stat Prob Lett"},{"issue":"6","key":"909_CR30","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1002\/j.1538-7305.1957.tb01515.x","volume":"36","author":"RC Prim","year":"1957","unstructured":"Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36(6):1389\u20131401. https:\/\/doi.org\/10.1002\/j.1538-7305.1957.tb01515.x","journal-title":"Bell Syst Tech J"},{"key":"909_CR31","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.neuroimage.2014.10.015","volume":"104","author":"P Tewarie","year":"2015","unstructured":"Tewarie P, van Dellen E, Hillebrand A, Stam CJ (2015) The minimum spanning tree: an unbiased method for brain network analysis. Neuroimage 104:177\u2013188. https:\/\/doi.org\/10.1016\/j.neuroimage.2014.10.015","journal-title":"Neuroimage"},{"issue":"4","key":"909_CR32","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1093\/bioinformatics\/18.4.536","volume":"18","author":"Y Xu","year":"2002","unstructured":"Xu Y, Olman V, Xu D (2002) Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees. Bioinformatics 18(4):536\u2013545. https:\/\/doi.org\/10.1093\/bioinformatics\/18.4.536","journal-title":"Bioinformatics"},{"issue":"01","key":"909_CR33","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1142\/S0218488515500038","volume":"23","author":"J Zhou","year":"2015","unstructured":"Zhou J, Chen L, Wang K (2015) Path optimality conditions for minimum spanning tree problem with uncertain edge weights. Internat J Uncertain Fuzziness Knowledge-Based Systems 23(01):49\u201371. https:\/\/doi.org\/10.1142\/S0218488515500038","journal-title":"Internat J Uncertain Fuzziness Knowledge-Based Systems"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-025-00909-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00186-025-00909-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-025-00909-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T12:42:26Z","timestamp":1775133746000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00186-025-00909-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,23]]},"references-count":33,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["909"],"URL":"https:\/\/doi.org\/10.1007\/s00186-025-00909-z","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,23]]},"assertion":[{"value":"15 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 October 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}