{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T13:20:16Z","timestamp":1780060816525,"version":"3.54.0"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Gromov\u2013Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov\u2013Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov\u2013Hausdorff (mGH) distance, a relaxation of the standard Gromov\u2013Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.<\/jats:p>","DOI":"10.1007\/s10878-024-01202-1","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T18:03:34Z","timestamp":1724436214000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient estimation of the modified Gromov\u2013Hausdorff distance between unweighted graphs"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8872-7463","authenticated-orcid":false,"given":"Vladyslav","family":"Oles","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nathan","family":"Lemons","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Panchenko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"issue":"2","key":"1202_CR1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.0030017","volume":"3","author":"S Achard","year":"2007","unstructured":"Achard S, Bullmore E (2007) Efficiency and cost of economical brain functional networks. PLoS Comput Biol 3(2):e17","journal-title":"PLoS Comput Biol"},{"issue":"10","key":"1202_CR2","doi-asserted-by":"publisher","first-page":"2942","DOI":"10.1073\/pnas.1401651112","volume":"112","author":"Y Aflalo","year":"2015","unstructured":"Aflalo Y, Bronstein A, Kimmel R (2015) On convex relaxation of graph isomorphism. Proc Natl Acad Sci 112(10):2942\u20132947","journal-title":"Proc Natl Acad Sci"},{"issue":"1","key":"1202_CR3","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","volume":"74","author":"R Albert","year":"2002","unstructured":"Albert R, Barab\u00e1si A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47","journal-title":"Rev Mod Phys"},{"issue":"8","key":"1202_CR4","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/S0167-8655(97)00060-3","volume":"18","author":"H Bunke","year":"1997","unstructured":"Bunke H (1997) On a relation between graph edit distance and maximum common subgraph. Pattern Recogn Lett 18(8):689\u2013694","journal-title":"Pattern Recogn Lett"},{"key":"1202_CR5","doi-asserted-by":"crossref","unstructured":"Bunke H, Dickinson P, Humm A, Irniger C, Kraetzl M (2006) Computer network monitoring and abnormal event detection using graph matching and multidimensional scaling. In: Industrial conference on data mining. Springer, pp 576\u2013590","DOI":"10.1007\/11790853_45"},{"key":"1202_CR6","doi-asserted-by":"crossref","unstructured":"Bunke H, Kraetzl M (2004) Classification and detection of abnormal events in time series of graphs. In: Data mining in time series databases. World Scientific, pp 127\u2013148","DOI":"10.1142\/9789812565402_0006"},{"key":"1202_CR7","doi-asserted-by":"crossref","unstructured":"Burkard RE, Cela E, Pardalos PM, Pitsoulis LS (1998) The quadratic assignment problem. In: Handbook of combinatorial optimization. Springer, pp 1713\u20131809","DOI":"10.1007\/978-1-4613-0303-9_27"},{"issue":"1","key":"1202_CR8","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0166-218X(85)90037-X","volume":"12","author":"RE Burkard","year":"1985","unstructured":"Burkard RE, Fincke U (1985) Probabilistic asymptotic properties of some combinatorial optimization problems. Discret Appl Math 12(1):21\u201329","journal-title":"Discret Appl Math"},{"issue":"2","key":"1202_CR9","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1023\/A:1007992709392","volume":"26","author":"E Calabi","year":"1998","unstructured":"Calabi E, Olver PJ, Shakiban C, Tannenbaum A, Haker S (1998) Differential and numerically invariant signature curves applied to object recognition. Int J Comput Vision 26(2):107\u2013135","journal-title":"Int J Comput Vision"},{"key":"1202_CR10","doi-asserted-by":"crossref","unstructured":"Chazal F, Cohen-Steiner D, Guibas LJ, M\u00e9moli F, Oudot SY (2009) Gromov-Hausdorff stable signatures for shapes using persistence. In: Computer graphics forum, vol\u00a028. Wiley Online Library, pp 1393\u20131403","DOI":"10.1111\/j.1467-8659.2009.01516.x"},{"issue":"2","key":"1202_CR11","first-page":"137","volume":"4","author":"M-S Cho","year":"1997","unstructured":"Cho M-S (1997) On the optimal covering of equal metric balls in a sphere. Pure Appl Math 4(2):137\u2013144","journal-title":"Pure Appl Math"},{"issue":"5","key":"1202_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.058701","volume":"90","author":"R Cohen","year":"2003","unstructured":"Cohen R, Havlin S (2003) Scale-free networks are ultrasmall. Phys Rev Lett 90(5):058701","journal-title":"Phys Rev Lett"},{"issue":"30","key":"1202_CR13","doi-asserted-by":"publisher","first-page":"845","DOI":"10.21105\/joss.00845","volume":"3","author":"V Constantinou","year":"2018","unstructured":"Constantinou V (2018) PyNomaly: anomaly detection using local outlier probabilities (loOP). J Open Source Softw 3(30):845","journal-title":"J Open Source Softw"},{"issue":"03","key":"1202_CR14","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1142\/S0218001404003228","volume":"18","author":"D Conte","year":"2004","unstructured":"Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching in pattern recognition. Int J Pattern Recognit Artif Intell 18(03):265\u2013298","journal-title":"Int J Pattern Recognit Artif Intell"},{"issue":"6","key":"1202_CR15","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1038\/mp.2013.78","volume":"19","author":"A Di\u00a0Martino","year":"2014","unstructured":"Di\u00a0Martino A, Yan C-G, Li Q, Denio E, Castellanos FX, Alaerts K, Anderson JS, Assaf M, Bookheimer SY, Dapretto M et al (2014) The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism. Mol Psychiatry 19(6):659\u2013667","journal-title":"Mol Psychiatry"},{"issue":"01","key":"1202_CR16","doi-asserted-by":"publisher","first-page":"1450001","DOI":"10.1142\/S0218001414500013","volume":"28","author":"P Foggia","year":"2014","unstructured":"Foggia P, Percannella G, Vento M (2014) Graph matching and learning in pattern recognition in the last 10 years. Int J Pattern Recognit Artif Intell 28(01):1450001","journal-title":"Int J Pattern Recognit Artif Intell"},{"issue":"2","key":"1202_CR17","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1137\/0110022","volume":"10","author":"PC Gilmore","year":"1962","unstructured":"Gilmore PC (1962) Optimal and suboptimal algorithms for the quadratic assignment problem. J Soc Ind Appl Math 10(2):305\u2013313","journal-title":"J Soc Ind Appl Math"},{"key":"1202_CR18","unstructured":"Gromov M (2007) Metric structures for Riemannian and non-Riemannian spaces. Springer"},{"issue":"1","key":"1202_CR19","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/BF02698687","volume":"53","author":"M Gromov","year":"1981","unstructured":"Gromov M (1981) Groups of polynomial growth and expanding maps. Publications Math\u00e9matiques de l\u2019Institut des Hautes \u00c9tudes Scientifiques 53(1):53\u201378","journal-title":"Publications Math\u00e9matiques de l\u2019Institut des Hautes \u00c9tudes Scientifiques"},{"key":"1202_CR20","unstructured":"Hagberg A, Swart P, Chult Daniel S (2008) Exploring network structure, dynamics, and function using NetworkX. Technical report, Los Alamos National Lab.(LANL), Los Alamos, NM (United States)"},{"key":"1202_CR21","doi-asserted-by":"crossref","unstructured":"Heard N, Rubin-Delanchy P (2016) Network-wide anomaly detection via the Dirichlet process. In: 2016 IEEE conference on intelligence and security informatics (ISI). IEEE, pp 220\u2013224","DOI":"10.1109\/ISI.2016.7745478"},{"key":"1202_CR22","unstructured":"Hendrikson R et\u00a0al. (2016) Using Gromov-Wasserstein distance to explore sets of networks. University of Tartu, Master Thesis, 2"},{"key":"1202_CR23","doi-asserted-by":"crossref","unstructured":"Kalton NJ, Ostrovskii MI (1999) Distances between Banach spaces","DOI":"10.1515\/form.11.1.17"},{"issue":"6","key":"1202_CR24","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000100","volume":"4","author":"S Kaustubh","year":"2008","unstructured":"Kaustubh S, Vinod M, Daniel R, Mark M, Greicius Michael D (2008) Network analysis of intrinsic functional brain connectivity in Alzheimer\u2019s disease. PLoS Comput Biol 4(6):e1000100","journal-title":"PLoS Comput Biol"},{"key":"1202_CR25","doi-asserted-by":"publisher","first-page":"1018","DOI":"10.3389\/fnins.2018.01018","volume":"12","author":"A Kazeminejad","year":"2019","unstructured":"Kazeminejad A, Sotero RC (2019) Topological properties of resting-state fMRI functional networks improve machine learning-based autism classification. Front Neurosci 12:1018","journal-title":"Front Neurosci"},{"key":"1202_CR26","unstructured":"K\u00e9gl B (2002) Intrinsic dimension estimation using packing numbers. In: NIPS. Citeseer, pp 681\u2013688"},{"key":"1202_CR27","doi-asserted-by":"crossref","unstructured":"Kent AD (2016) Cyber security data sources for dynamic network research. In: Dynamic networks and cyber-security. World Scientific, pp 37\u201365","DOI":"10.1142\/9781786340757_0002"},{"key":"1202_CR28","doi-asserted-by":"crossref","unstructured":"Klimt B, Yang Y (2004) The enron corpus: a new dataset for email classification research. In: European conference on machine learning. Springer, pp 217\u2013226","DOI":"10.1007\/978-3-540-30115-8_22"},{"key":"1202_CR29","doi-asserted-by":"crossref","unstructured":"Koutra D, Vogelstein JT, Faloutsos C (2013) Deltacon: a principled massive-graph similarity function. In: Proceedings of the 2013 SIAM international conference on data mining. SIAM, pp 162\u2013170","DOI":"10.1137\/1.9781611972832.18"},{"key":"1202_CR30","doi-asserted-by":"crossref","unstructured":"Kriegel H-P, Kr\u00f6ger P, Schubert E, Zimek A (2009) LoOP: local outlier probabilities. In: Proceedings of the 18th ACM conference on information and knowledge management, pp 1649\u20131652","DOI":"10.1145\/1645953.1646195"},{"key":"1202_CR31","first-page":"2381","volume":"12","author":"H Lee","year":"2006","unstructured":"Lee H, Chung MK, Kang H, Kim B-N, Lee DS et al (2006) Persistent network homology from the perspective of dendrograms. IEEE Trans Med Imaging 12:2381\u20132381","journal-title":"IEEE Trans Med Imaging"},{"key":"1202_CR32","doi-asserted-by":"crossref","unstructured":"Lee H, Chung MK, Kang H, Kim B-N, Lee DS (2011) Computing the shape of brain networks using graph filtration and Gromov-Hausdorff metric. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 302\u2013309","DOI":"10.1007\/978-3-642-23629-7_37"},{"issue":"3","key":"1202_CR33","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1016\/j.aim.2011.01.020","volume":"227","author":"Y Lipman","year":"2011","unstructured":"Lipman Y, Daubechies I (2011) Conformal Wasserstein distances: comparing surfaces in polynomial time. Adv Math 227(3):1047\u20131077","journal-title":"Adv Math"},{"key":"1202_CR34","unstructured":"Majhi S, Vitter J, Wenk C (2019) Approximating Gromov-Hausdorff distance in euclidean space. arXiv:1912.13008"},{"key":"1202_CR35","doi-asserted-by":"crossref","unstructured":"M\u00e9moli F (2007) On the use of Gromov-Hausdorff distances for shape comparison","DOI":"10.1109\/CVPRW.2008.4563074"},{"key":"1202_CR36","doi-asserted-by":"crossref","unstructured":"M\u00e9moli F (2009) Spectral Gromov-Wasserstein distances for shape matching. In: 2009 IEEE 12th international conference on computer vision workshops, ICCV Workshops. IEEE, pp 256\u2013263","DOI":"10.1109\/ICCVW.2009.5457690"},{"issue":"4","key":"1202_CR37","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s10208-011-9093-5","volume":"11","author":"F M\u00e9moli","year":"2011","unstructured":"M\u00e9moli F (2011) Gromov-Wasserstein distances and the metric approach to object matching. Found Comput Math 11(4):417\u2013487","journal-title":"Found Comput Math"},{"issue":"2","key":"1202_CR38","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/s00454-012-9406-8","volume":"48","author":"F M\u00e9moli","year":"2012","unstructured":"M\u00e9moli F (2012) Some properties of Gromov-Hausdorff distances. Discrete Comput Geom 48(2):416\u2013440","journal-title":"Discrete Comput Geom"},{"issue":"1","key":"1202_CR39","doi-asserted-by":"publisher","first-page":"89","DOI":"10.5802\/acirm.58","volume":"3","author":"F M\u00e9moli","year":"2013","unstructured":"M\u00e9moli F (2013) The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects. Actes des rencontres du CIRM 3(1):89\u201396","journal-title":"Actes des rencontres du CIRM"},{"key":"1202_CR40","doi-asserted-by":"crossref","unstructured":"M\u00e9moli F, Sapiro G (2004) Comparing point clouds. In: Proceedings of the 2004 Eurographics\/ACM SIGGRAPH symposium on Geometry processing, pp 32\u201340","DOI":"10.1145\/1057432.1057436"},{"key":"1202_CR41","unstructured":"Oles V, Vixie KR (2022) Lipschitz (non-)equivalence of the Gromov\u2013Hausdorff distances, including on ultrametric spaces. arXiv:2204.10250"},{"issue":"2","key":"1202_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3185466","volume":"14","author":"KA Pankaj","year":"2018","unstructured":"Pankaj KA, Kyle F, Abhinandan N, Anastasios S, Yusu W (2018) Computing the Gromov-Hausdorff distance for metric trees. ACM Trans Algorithms (TALG) 14(2):1\u201320","journal-title":"ACM Trans Algorithms (TALG)"},{"key":"1202_CR43","unstructured":"Peyr\u00e9 G, Cuturi M, Solomon J (2016) Gromov-Wasserstein averaging of kernel and distance matrices. In: International conference on machine learning. PMLR, pp 2664\u20132672"},{"issue":"4","key":"1202_CR44","first-page":"2","volume":"24","author":"B Pincombe","year":"2005","unstructured":"Pincombe B (2005) Anomaly detection in time series of graphs using arma processes. Asor Bull 24(4):2","journal-title":"Asor Bull"},{"issue":"7","key":"1202_CR45","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1023\/A:1021271615909","volume":"16","author":"JW Raymond","year":"2002","unstructured":"Raymond JW, Willett P (2002) Maximum common subgraph isomorphism algorithms for the matching of chemical structures. J Comput Aided Mol Des 16(7):521\u2013533","journal-title":"J Comput Aided Mol Des"},{"key":"1202_CR46","doi-asserted-by":"publisher","first-page":"573","DOI":"10.3389\/fnhum.2013.00573","volume":"7","author":"E Redcay","year":"2013","unstructured":"Redcay E, Moran JM, Mavros PL, Tager-Flusberg H, Gabrieli JDE, Whitfield-Gabrieli S (2013) Intrinsic functional network organization in high-functioning adolescents with autism spectrum disorder. Front Hum Neurosci 7:573","journal-title":"Front Hum Neurosci"},{"issue":"3","key":"1202_CR47","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1016\/j.neuroimage.2009.10.003","volume":"52","author":"M Rubinov","year":"2010","unstructured":"Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3):1059\u20131069","journal-title":"Neuroimage"},{"key":"1202_CR48","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.nicl.2012.11.006","volume":"2","author":"JD Rudie","year":"2013","unstructured":"Rudie JD, Brown JA, Devi B-P, Hernandez LM, Dennis EL, Thompson PM, Bookheimer SY, Dapretto MJNC (2013) Altered functional and structural brain network organization in autism. NeuroImage Clin 2:79\u201394","journal-title":"NeuroImage Clin"},{"key":"1202_CR49","doi-asserted-by":"publisher","unstructured":"Saul N, Tralie C (2019) Scikit-TDA: topological data analysis for python. https:\/\/doi.org\/10.5281\/zenodo.2533369","DOI":"10.5281\/zenodo.2533369"},{"issue":"4","key":"1202_CR50","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1007\/s00454-017-9889-4","volume":"57","author":"F Schmiedl","year":"2017","unstructured":"Schmiedl F (2017) Computational aspects of the Gromov-Hausdorff distance and its application in non-rigid shape matching. Discrete Comput Geom 57(4):854","journal-title":"Discrete Comput Geom"},{"issue":"01n02","key":"1202_CR51","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1142\/S0219265902000562","volume":"3","author":"P Shoubridge","year":"2002","unstructured":"Shoubridge P, Kraetzl M, Wallis WAL, Bunke H (2002) Detection of abnormal change in a time series of graphs. J Interconnection Netw 3(01n02):85\u2013101","journal-title":"J Interconnection Netw"},{"issue":"1","key":"1202_CR52","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s11511-006-0002-8","volume":"196","author":"K-T Sturm","year":"2006","unstructured":"Sturm K-T (2006) On the geometry of metric measure spaces. Acta Math 196(1):65\u2013131","journal-title":"Acta Math"},{"key":"1202_CR53","doi-asserted-by":"crossref","unstructured":"Sulo R, Berger-Wolf T, Grossman R (2010) Meaningful selection of temporal resolution for dynamic networks. In: Proceedings of the eighth workshop on mining and learning with graphs, pp 127\u2013136","DOI":"10.1145\/1830252.1830269"},{"key":"1202_CR54","unstructured":"Tuzhilin AA (2016) Who invented the Gromov-Hausdorff distance? arXiv:1612.00728"},{"issue":"1","key":"1202_CR55","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1006\/nimg.2001.0978","volume":"15","author":"N Tzourio-Mazoyer","year":"2002","unstructured":"Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N, Mazoyer B, Joliot M (2002) Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15(1):273\u2013289","journal-title":"Neuroimage"},{"issue":"1","key":"1202_CR56","first-page":"113","volume":"4","author":"R van der Hofstad","year":"2007","unstructured":"van der Hofstad R, Hooghiemstra G, Znamenski D (2007) A phase transition for the diameter of the configuration model. Int Math 4(1):113\u2013128","journal-title":"Int Math"},{"issue":"10","key":"1202_CR57","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0013701","volume":"5","author":"CM Van Wijk Bernadette","year":"2010","unstructured":"Van Wijk Bernadette CM, Stam Cornelis J, Andreas D (2010) Comparing brain networks of different size and connectivity density using graph theory. PloS one 5(10):e13701","journal-title":"PloS one"},{"key":"1202_CR58","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1016\/j.cej.2012.07.014","volume":"207","author":"NM Vandewiele","year":"2012","unstructured":"Vandewiele NM, Van Geem KM, Reyniers M-F, Marin GB (2012) Kinetic model construction using chemo-informatics. Genesyst Chem Eng J 207:526\u2013538","journal-title":"Genesyst Chem Eng J"},{"key":"1202_CR59","doi-asserted-by":"crossref","unstructured":"Villani C (2003) Topics in optimal transportation, vol 58. American Mathematical Soc","DOI":"10.1090\/gsm\/058"},{"key":"1202_CR60","unstructured":"Villar S, Bandeira AS, Blumberg AJ, Ward R (2016) A polynomial-time relaxation of the Gromov-Hausdorff distance. arXiv:1610.05214"},{"issue":"6684","key":"1202_CR61","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1038\/30918","volume":"393","author":"DJ Watts","year":"1998","unstructured":"Watts DJ, Strogatz SH (1998) Collective dynamics of \u2018small-world\u2019networks. Nature 393(6684):440\u2013442","journal-title":"Nature"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01202-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-024-01202-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01202-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,25]],"date-time":"2024-09-25T20:52:58Z","timestamp":1727297578000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-024-01202-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,23]]},"references-count":61,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["1202"],"URL":"https:\/\/doi.org\/10.1007\/s10878-024-01202-1","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,23]]},"assertion":[{"value":"4 June 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 August 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"14"}}