{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T02:17:03Z","timestamp":1777429023833,"version":"3.51.4"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,2,2]],"date-time":"2020-02-02T00:00:00Z","timestamp":1580601600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,2]],"date-time":"2020-02-02T00:00:00Z","timestamp":1580601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1422400"],"award-info":[{"award-number":["1422400"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1526513"],"award-info":[{"award-number":["1526513"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1723003"],"award-info":[{"award-number":["1723003"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1740761"],"award-info":[{"award-number":["1740761"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00454-019-00168-w","type":"journal-article","created":{"date-parts":[[2020,2,2]],"date-time":"2020-02-02T01:02:36Z","timestamp":1580605356000},"page":"831-875","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Spatiotemporal Persistent Homology for Dynamic Metric Spaces"],"prefix":"10.1007","volume":"66","author":[{"given":"Woojin","family":"Kim","sequence":"first","affiliation":[]},{"given":"Facundo","family":"M\u00e9moli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,2]]},"reference":[{"key":"168_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/978-3-662-48971-0_45","volume-title":"International Symposium on Algorithms and Computation","author":"PK Agarwal","year":"2015","unstructured":"Agarwal, P.K., Fox, K., Nath, A., Sidiropoulos, A., Wang, Y.: Computing the Gromov\u2013Hausdorff distance for metric trees. International Symposium on Algorithms and Computation. Lecture Notes in Computer Science, vol. 9472, pp. 529\u2013540. Springer, Heidelberg (2015)"},{"issue":"9","key":"168_CR2","doi-asserted-by":"crossref","first-page":"e1006433","DOI":"10.1371\/journal.pcbi.1006433","volume":"14","author":"A Babichev","year":"2018","unstructured":"Babichev, A., Morozov, D., Dabaghian, Y.: Robust spatial memory maps encoded by networks with transient connections. PLoS Comput. Biol. 14(9), e1006433 (2018)","journal-title":"PLoS Comput. Biol."},{"key":"168_CR3","unstructured":"Bauer, U., Edelsbrunner, H., Jablonski, G., Mrozek, M.: Persistence in sampled dynamical systems faster. arXiv preprint arXiv:1709.04068 (2017)"},{"issue":"1","key":"168_CR4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.4310\/HHA.2013.v15.n1.a3","volume":"15","author":"P Bendich","year":"2013","unstructured":"Bendich, P., Edelsbrunner, H., Morozov, D., Patel, A.: Homology and robustness of level and interlevel sets. Homology Homotopy Appl. 15(1), 51\u201372 (2013)","journal-title":"Homology Homotopy Appl."},{"issue":"3","key":"168_CR5","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.comgeo.2007.10.003","volume":"41","author":"M Benkert","year":"2008","unstructured":"Benkert, M., Gudmundsson, J., H\u00fcbner, F., Wolle, T.: Reporting flock patterns. Comput. Geom. 41(3), 111\u2013125 (2008)","journal-title":"Comput. Geom."},{"issue":"14","key":"168_CR6","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1016\/j.patrec.2011.07.014","volume":"32","author":"S Biasotti","year":"2011","unstructured":"Biasotti, S., Cerri, A., Frosini, P., Giorgi, D.: A new algorithm for computing the 2-dimensional matching distance between size functions. Pattern Recognit. Lett. 32(14), 1735\u20131746 (2011)","journal-title":"Pattern Recognit. Lett."},{"key":"168_CR7","unstructured":"Bjerkevik, H.B., Botnan, M.B.: Computational complexity of the interleaving distance. In: Proceedings of the 34th International Symposium on Computational Geometry (SoCG 2018), pp. 13:1\u201313:15 (2018)"},{"key":"168_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-019-09442-y","author":"HB Bjerkevik","year":"2019","unstructured":"Bjerkevik, H.B., Botnan, M.B., Kerber, M.: Computing the interleaving distance is NP-hard. Found. Comput. Math. (2019). https:\/\/doi.org\/10.1007\/s10208-019-09442-y","journal-title":"Found. Comput. Math."},{"issue":"6","key":"168_CR9","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.2140\/agt.2018.18.3133","volume":"18","author":"M Botnan","year":"2018","unstructured":"Botnan, M., Lesnick, M.: Algebraic stability of zigzag persistence modules. Algebra. Geom. Topol. 18(6), 3133\u20133204 (2018)","journal-title":"Algebra. Geom. Topol."},{"issue":"3","key":"168_CR10","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1007\/s00454-014-9573-x","volume":"51","author":"P Bubenik","year":"2014","unstructured":"Bubenik, P., Scott, J.A.: Categorification of persistent homology. Discrete Comput. Geom. 51(3), 600\u2013627 (2014)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"168_CR11","first-page":"75","volume":"6","author":"K Buchin","year":"2015","unstructured":"Buchin, K., Buchin, M., van Kreveld, M.J., Speckmann, B., Staals, F.: Trajectory grouping structure. JoCG 6(1), 75\u201398 (2015)","journal-title":"JoCG"},{"key":"168_CR12","doi-asserted-by":"crossref","unstructured":"Burago, D., Burago, Yu., Ivanov, S.: A Course in Metric Geometry, vol. 33. American Mathematical Society, Providence (2001)","DOI":"10.1090\/gsm\/033"},{"key":"168_CR13","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1090\/S0273-0979-09-01249-X","volume":"46","author":"G Carlsson","year":"2009","unstructured":"Carlsson, G.: Topology and data. Bull. Am. Math. Soc. 46, 255\u2013308 (2009)","journal-title":"Bull. Am. Math. Soc."},{"issue":"4","key":"168_CR14","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s10208-010-9066-0","volume":"10","author":"G Carlsson","year":"2010","unstructured":"Carlsson, G., de Silva, V.: Zigzag persistence. Found. Comput. Math. 10(4), 367\u2013405 (2010)","journal-title":"Found. Comput. Math."},{"key":"168_CR15","doi-asserted-by":"crossref","unstructured":"Carlsson, G., de Silva, V., Morozov, D.: Zigzag persistent homology and real-valued functions. In: Proceedings of the 25th Annual Symposium on Computational Geometry, pp. 247\u2013256. ACM (2009)","DOI":"10.1145\/1542362.1542408"},{"key":"168_CR16","first-page":"1425","volume":"11","author":"G Carlsson","year":"2010","unstructured":"Carlsson, G., M\u00e9moli, F.: Characterization, stability and convergence of hierarchical clustering methods. J. Mach. Learn. Res. 11, 1425\u20131470 (2010)","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"168_CR17","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s00454-009-9176-0","volume":"42","author":"G Carlsson","year":"2009","unstructured":"Carlsson, G., Zomorodian, A.: The theory of multidimensional persistence. Discrete Comput. Geom. 42(1), 71\u201393 (2009)","journal-title":"Discrete Comput. Geom."},{"key":"168_CR18","doi-asserted-by":"crossref","unstructured":"Cerri, A., Di Fabio, B., Ferri, M., Frosini, P., Landi, C.: Betti numbers in multidimensional persistent homology are stable functions. Math. Methods Appl. Sci. 36(12), 1543\u20131557 (2013)","DOI":"10.1002\/mma.2704"},{"key":"168_CR19","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.cviu.2013.11.004","volume":"121","author":"A Cerri","year":"2014","unstructured":"Cerri, A., Di Fabio, B., Jab\u0142o\u0144ski, G., Medri, F.: Comparing shapes through multi-scale approximations of the matching distance. Comput. Vis. Image Understand. 121, 43\u201356 (2014)","journal-title":"Comput. Vis. Image Understand."},{"key":"168_CR20","unstructured":"Cerri, A., Frosini, P.: A new approximation algorithm for the matching distance in multidimensional persistence. (2011)"},{"key":"168_CR21","doi-asserted-by":"crossref","unstructured":"Chazal, F., Cohen-Steiner, D., Glisse, M., Guibas, L.J., Oudot, S.: Proximity of persistence modules and their diagrams. In: Proceeding of 25th ACM Symposium on Computational Geometry, pp. 237\u2013246 (2009)","DOI":"10.1145\/1542362.1542407"},{"key":"168_CR22","doi-asserted-by":"crossref","unstructured":"Chazal, F., Cohen-Steiner, D., Guibas, L.J., M\u00e9moli, F., Oudot, S.Y.: Gromov\u2013Hausdorff stable signatures for shapes using persistence. In: Proceedings of SGP (2009)","DOI":"10.1111\/j.1467-8659.2009.01516.x"},{"issue":"1","key":"168_CR23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10711-013-9937-z","volume":"173","author":"F Chazal","year":"2014","unstructured":"Chazal, F., De Silva, V., Oudot, S.: Persistence stability for geometric complexes. Geom. Dedicata 173(1), 193\u2013214 (2014)","journal-title":"Geom. Dedicata"},{"issue":"1","key":"168_CR24","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00454-006-1276-5","volume":"37","author":"D Cohen-Steiner","year":"2007","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discrete Comput. Geom. 37(1), 103\u2013120 (2007)","journal-title":"Discrete Comput. Geom."},{"key":"168_CR25","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Morozov, D.: Vines and vineyards by updating persistence in linear time. In: Proceedings of the 22nd Annual Symposium on Computational Geometry, pp. 119\u2013126. ACM (2006)","DOI":"10.1145\/1137856.1137877"},{"issue":"4","key":"168_CR26","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1007\/s00454-016-9763-9","volume":"55","author":"V De Silva","year":"2016","unstructured":"De Silva, V., Munch, E., Patel, A.: Categorified Reeb graphs. Discrete Comput. Geom. 55(4), 854\u2013906 (2016)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"168_CR27","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1137\/18M1198946","volume":"18","author":"TK Dey","year":"2019","unstructured":"Dey, T.K., Juda, M., Kapela, T., Kubica, J., Lipi\u0144ski, M., Mrozek, M.: Persistent homology of morse decompositions in combinatorial dynamics. SIAM J. Appl. Dyn. Syst. 18(1), 510\u2013530 (2019)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"168_CR28","unstructured":"Dey, T.K., Xin, C.: Computing bottleneck distance for 2-D interval decomposable modules. In: Proceedings of the Thirty-Fourth International Symposium on Computational Geometry (SoCG 2018), pp. 32:1\u201332:15 (2018)"},{"key":"168_CR29","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1090\/conm\/453\/08802","volume":"453","author":"H Edelsbrunner","year":"2008","unstructured":"Edelsbrunner, H., Harer, J.: Persistent homology: a survey. Contemp. Math. 453, 257\u2013282 (2008)","journal-title":"Contemp. Math."},{"key":"168_CR30","volume-title":"Computational Topology: An Introduction","author":"H Edelsbrunner","year":"2010","unstructured":"Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society, Providence (2010)"},{"issue":"3","key":"168_CR31","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.comgeo.2007.11.001","volume":"41","author":"H Edelsbrunner","year":"2008","unstructured":"Edelsbrunner, H., Harer, J., Mascarenhas, A., Pascucci, V., Snoeyink, J.: Time-varying Reeb graphs for continuous space-time data. Comput. Geom. 41(3), 149\u2013166 (2008)","journal-title":"Comput. Geom."},{"issue":"5","key":"168_CR32","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1007\/s10208-014-9223-y","volume":"15","author":"H Edelsbrunner","year":"2015","unstructured":"Edelsbrunner, H., Jab\u0142o\u0144ski, G., Mrozek, M.: The persistent homology of a self-map. Found. Comput. Math. 15(5), 1213\u20131244 (2015)","journal-title":"Found. Comput. Math."},{"issue":"1","key":"168_CR33","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1090\/S0273-0979-07-01191-3","volume":"45","author":"R Ghrist","year":"2008","unstructured":"Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61\u201375 (2008)","journal-title":"Bull. Am. Math. Soc."},{"issue":"1","key":"168_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10827-016-0608-6","volume":"41","author":"C Giusti","year":"2016","unstructured":"Giusti, C., Ghrist, R., Bassett, D.S.: Two\u2019s company, three (or more) is a simplex. J. Comput. Neurosci. 41(1), 1\u201314 (2016)","journal-title":"J. Comput. Neurosci."},{"issue":"44","key":"168_CR35","doi-asserted-by":"crossref","first-page":"13455","DOI":"10.1073\/pnas.1506407112","volume":"112","author":"C Giusti","year":"2015","unstructured":"Giusti, C., Pastalkova, E., Curto, C., Itskov, V.: Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Natl. Acad. Sci. 112(44), 13455\u201313460 (2015)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"168_CR36","doi-asserted-by":"crossref","unstructured":"Gudmundsson, J., van Kreveld, M.: Computing longest duration flocks in trajectory data. In: Proceedings of the 14th Annual ACM International Symposium on Advances in Geographic Information Systems, pp. 35\u201342. ACM (2006)","DOI":"10.1145\/1183471.1183479"},{"issue":"2","key":"168_CR37","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10707-006-0002-z","volume":"11","author":"J Gudmundsson","year":"2007","unstructured":"Gudmundsson, J., van Kreveld, M., Speckmann, B.: Efficient detection of patterns in 2d trajectories of moving points. Geoinformatica 11(2), 195\u2013215 (2007)","journal-title":"Geoinformatica"},{"key":"168_CR38","doi-asserted-by":"crossref","unstructured":"Hajij, M., Wang, B., Scheidegger, C., Rosen, P.: Visual detection of structural changes in time-varying graphs using persistent homology. In: Pacific Visualization Symposium (PacificVis), 2018 IEEE, pp. 125\u2013134. IEEE (2018)","DOI":"10.1109\/PacificVis.2018.00024"},{"key":"168_CR39","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/978-3-540-87473-7_6","volume-title":"International Conference on Geographic Information Science","author":"Y Huang","year":"2008","unstructured":"Huang, Y., Chen, C., Dong, P.: Modeling herds and their evolvements from trajectory data. International Conference on Geographic Information Science, pp. 90\u2013105. Springer, New York (2008)"},{"key":"168_CR40","first-page":"713","volume-title":"PAKDD","author":"S-Y Hwang","year":"2005","unstructured":"Hwang, S.-Y., Liu, Y.-H., Chiu, J.-K., Lim, E.-P.: Mining mobile group patterns: a trajectory-based approach. PAKDD, vol. 3518, pp. 713\u2013718. Springer, New York (2005)"},{"issue":"1","key":"168_CR41","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.14778\/1453856.1453971","volume":"1","author":"H Jeung","year":"2008","unstructured":"Jeung, H., Yiu, M.L., Zhou, X., Jensen, C.S., Shen, H.T.: Discovery of convoys in trajectory databases. Proc. VLDB Endow. 1(1), 1068\u20131080 (2008)","journal-title":"Proc. VLDB Endow."},{"key":"168_CR42","doi-asserted-by":"crossref","unstructured":"Kahle, M., Meckes, E.: Limit the theorems for Betti numbers of random simplicial complexes. Homology Homotopy Appl. 15(1), 343\u2013374 (2013)","DOI":"10.4310\/HHA.2013.v15.n1.a17"},{"key":"168_CR43","first-page":"364","volume-title":"SSTD","author":"P Kalnis","year":"2005","unstructured":"Kalnis, P., Mamoulis, N., Bakiras, S.: On discovering moving clusters in spatio-temporal data. SSTD, vol. 3633, pp. 364\u2013381. Springer, Berlin (2005)"},{"key":"168_CR44","unstructured":"Kerber, M., Lesnick, M., Oudot, S.: Exact computation of the matching distance on 2-parameter persistence modules. In: Proceedings of the 35th International Symposium on Computational Geometry, pp. 46:1\u201346:15 (2019)"},{"key":"168_CR45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3064175","volume":"22","author":"M Kerber","year":"2017","unstructured":"Kerber, M., Morozov, D., Nigmetov, A.: Geometry helps to compare persistence diagrams. J. Exp. Algorithm. 22, 1\u20134 (2017)","journal-title":"J. Exp. Algorithm."},{"key":"168_CR46","unstructured":"Kim, W., M\u00e9moli, F.: Stable signatures for dynamic graphs and dynamic metric spaces via zigzag persistence. arXiv preprint arXiv:1712.04064 (2017)"},{"key":"168_CR47","unstructured":"Kim, W., M\u00e9moli, F.: Formigrams: Clustering summaries of dynamic data. In: Proceedings of 30th Canadian Conference on Computational Geometry (CCCG18) (2018)"},{"key":"168_CR48","unstructured":"Kim, W., M\u00e9moli, F., Smith, Z.: https:\/\/research.math.osu.edu\/networks\/formigrams"},{"issue":"6","key":"168_CR49","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1137\/0217076","volume":"17","author":"WJ Knight","year":"1988","unstructured":"Knight, W.J.: Search in an ordered array having variable probe cost. SIAM J. Comput. 17(6), 1203\u20131214 (1988)","journal-title":"SIAM J. Comput."},{"key":"168_CR50","unstructured":"Kostitsyna, I., van Kreveld, M.J., L\u00f6ffler, M., Speckmann, B., Staals, F.: Trajectory grouping structure under geodesic distance. In: 31st International Symposium on Computational Geometry, SoCG 2015, June 22\u201325, 2015, Eindhoven, The Netherlands, pp. 674\u2013688 (2015)"},{"key":"168_CR51","first-page":"1","volume-title":"Research in Computational Topology","author":"C Landi","year":"2018","unstructured":"Landi, C.: The rank invariant stability via interleavings. Research in Computational Topology, pp. 1\u201310. Springer, Berlin (2018)"},{"issue":"3","key":"168_CR52","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s10208-015-9255-y","volume":"15","author":"M Lesnick","year":"2015","unstructured":"Lesnick, M.: The theory of the interleaving distance on multidimensional persistence modules. Found. Comput. Math. 15(3), 613\u2013650 (2015)","journal-title":"Found. Comput. Math."},{"issue":"1\u20132","key":"168_CR53","doi-asserted-by":"crossref","first-page":"723","DOI":"10.14778\/1920841.1920934","volume":"3","author":"Z Li","year":"2010","unstructured":"Li, Z., Ding, B., Han, J., Kays, R.: Swarm: mining relaxed temporal moving object clusters. Proc. VLDB Endow. 3(1\u20132), 723\u2013734 (2010)","journal-title":"Proc. VLDB Endow."},{"key":"168_CR54","series-title":"Graduate Texts in Mathematics","volume-title":"Categories for the Working Mathematician","author":"S Mac Lane","year":"2013","unstructured":"Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, vol. 5. Springer, New York (2013)"},{"key":"168_CR55","unstructured":"Munch, E.: Applications of persistent homology to time varying systems. PhD thesis (2013)"},{"key":"168_CR56","first-page":"87","volume-title":"Topological Methods in Data Analysis and Visualization","author":"P Oesterling","year":"2015","unstructured":"Oesterling, P., Heine, C., Weber, G.H., Morozov, D., Scheuermann, G.: Computing and visualizing time-varying merge trees for high-dimensional data. Topological Methods in Data Analysis and Visualization, pp. 87\u2013101. Springer, Berlin (2015)"},{"key":"168_CR57","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511601156","volume-title":"Animal Groups in Three Dimensions: How Species Aggregate","author":"J\u00a0K Parrish","year":"1997","unstructured":"Parrish, J\u00a0.K., Hamner, W\u00a0M\u00a0e: Animal Groups in Three Dimensions: How Species Aggregate. Cambridge University Press, Cambridge (1997)"},{"key":"168_CR58","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s41468-018-0012-6","volume":"1","author":"A Patel","year":"2018","unstructured":"Patel, A.: Generalized persistence diagrams. J. Appl. Comput. Topol. 1, 397\u2013419 (2018)","journal-title":"J. Appl. Comput. Topol."},{"key":"168_CR59","unstructured":"Puuska, V.: Erosion distance for generalized persistence modules. arXiv preprint arXiv:1710.01577 (2017)"},{"key":"168_CR60","unstructured":"Schmiedl, F.: Shape Matching and Mesh Segmentation. PhD thesis, Technische Universit\u00e4t M\u00fcnchen (2014)"},{"issue":"4","key":"168_CR61","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1007\/s00454-017-9889-4","volume":"57","author":"F Schmiedl","year":"2017","unstructured":"Schmiedl, F.: Computational aspects of the Gromov\u2013Hausdorff distance and its application in non-rigid shape matching. Discrete Comput. Geom. 57(4), 854\u2013880 (2017)","journal-title":"Discrete Comput. Geom."},{"issue":"6","key":"168_CR62","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1007\/s10208-016-9323-y","volume":"17","author":"M Scolamiero","year":"2017","unstructured":"Scolamiero, M., Chach\u00f3lski, W., Lundman, A., Ramanujam, R., \u00d6berg, S.: Multidimensional persistence and noise. Found. Comput. Math. 17(6), 1367\u20131406 (2017)","journal-title":"Found. Comput. Math."},{"key":"168_CR63","doi-asserted-by":"crossref","DOI":"10.1515\/9781400837106","volume-title":"Collective Animal Bbehavior","author":"DJ Sumpter","year":"2010","unstructured":"Sumpter, D.J.: Collective Animal Bbehavior. Princeton University Press, Princeton (2010)"},{"issue":"5","key":"168_CR64","doi-asserted-by":"crossref","first-page":"e0126383","DOI":"10.1371\/journal.pone.0126383","volume":"10","author":"CM Topaz","year":"2015","unstructured":"Topaz, C.M., Ziegelmeier, L., Halverson, T.: Topological data analysis of biological aggregation models. PloS ONE 10(5), e0126383 (2015)","journal-title":"PloS ONE"},{"key":"168_CR65","unstructured":"Ulmer, M., Ziegelmeier, L., Topaz, C.M.: Assessing biological models using topological data analysis. arXiv preprint arXiv:1811.04827 (2018)"},{"key":"168_CR66","unstructured":"van Goethem, A., van Kreveld, M.J., L\u00f6ffler, M., Speckmann, B., Staals, F.: Grouping time-varying data for interactive exploration. In: 32nd International Symposium on Computational Geometry, SoCG 2016, June 14\u201318, 2016, Boston, MA, USA, pp. 61:1\u201361:16 (2016)"},{"issue":"1","key":"168_CR67","first-page":"366","volume":"8","author":"MJ van Kreveld","year":"2017","unstructured":"van Kreveld, M.J., L\u00f6ffler, M., Staals, F.: Central trajectories. J. Comput. Geom. 8(1), 366\u2013386 (2017)","journal-title":"J. Comput. Geom."},{"key":"168_CR68","unstructured":"van Kreveld, M.J., L\u00f6ffler, M., Staals, F., Wiratma, L.: A refined definition for groups of moving entities and its computation. In: 27th International Symposium on Algorithms and Computation, ISAAC 2016, December 12\u201314, 2016, Sydney, Australia, pp. 48:1\u201348:12 (2016)"},{"key":"168_CR69","doi-asserted-by":"crossref","unstructured":"Vieira, M.R., Bakalov, P., Tsotras, V.J.: On-line discovery of flock patterns in spatio-temporal data. In: Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 286\u2013295. ACM (2009)","DOI":"10.1145\/1653771.1653812"},{"issue":"3","key":"168_CR70","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00778-006-0019-9","volume":"17","author":"Y Wang","year":"2008","unstructured":"Wang, Y., Lim, E.-P., Hwang, S.-Y.: Efficient algorithms for mining maximal valid groups. VLDB J. 17(3), 515\u2013535 (2008)","journal-title":"VLDB J."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00168-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-019-00168-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00168-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T16:10:22Z","timestamp":1631203822000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-019-00168-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,2]]},"references-count":70,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["168"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00168-w","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,2]]},"assertion":[{"value":"1 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}