{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T09:54:08Z","timestamp":1726221248506},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T00:00:00Z","timestamp":1559174400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T00:00:00Z","timestamp":1559174400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"NSF","award":["1422400","1526513"],"award-info":[{"award-number":["1422400","1526513"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s00454-019-00104-y","type":"journal-article","created":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T15:03:01Z","timestamp":1559228581000},"page":"554-583","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Quantitative Simplification of Filtered Simplicial Complexes"],"prefix":"10.1007","volume":"65","author":[{"given":"Facundo","family":"M\u00e9moli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osman Berat","family":"Okutan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,30]]},"reference":[{"issue":"1","key":"104_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2140\/pjm.2017.290.1","volume":"290","author":"M Adamaszek","year":"2017","unstructured":"Adamaszek, M., Adams, H.: The Vietoris\u2013Rips complexes of a circle. Pac. J. Math. 290(1), 1\u201340 (2017)","journal-title":"Pac. J. Math."},{"key":"104_CR2","unstructured":"Adamaszek, M., Adams, H., Gasparovic, E., Gommel, M., Purvine, E., Sazdanovic, R., Wang, B., Wang, Y., Ziegelmeier, L.: Vietoris\u2013Rips and \u010cech complexes of metric gluings (2017). arXiv:1712.06224"},{"issue":"4","key":"104_CR3","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1142\/S0218195912600060","volume":"22","author":"D Attali","year":"2012","unstructured":"Attali, D., Lieutier, A., Salinas, D.: Efficient data structure for representing and simplifying simplicial complexes in high dimensions. Int. J. Comput. Geom. Appl. 22(4), 279\u2013303 (2012)","journal-title":"Int. J. Comput. Geom. Appl."},{"issue":"2","key":"104_CR4","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00454-011-9357-5","volume":"47","author":"JA Barmak","year":"2012","unstructured":"Barmak, J.A., Minian, E.G.: Strong homotopy types, nerves and collapses. Discrete Comput. Geom. 47(2), 301\u2013328 (2012)","journal-title":"Discrete Comput. Geom."},{"key":"104_CR5","doi-asserted-by":"crossref","unstructured":"Bauer, U., Lesnick, M.: Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the 30th Annual Symposium on Computational Geometry (SoCG\u201914), pp. 355\u2013364. ACM, New York (2014)","DOI":"10.1145\/2582112.2582168"},{"key":"104_CR6","unstructured":"Bauer, U., Munch, E., Wang, Y.: Strong equivalence of the interleaving and functional distortion metrics for Reeb graphs. In: Proceedings of the 31st International Symposium on Computational Geometry (SoCG\u201915). Leibniz International Proceedings in Informatics, vol. 34, pp. 461\u2013475. Schloss Dagstuhl. Leibniz-Zentrum f\u00fcr Informatik, Wadern (2015)"},{"key":"104_CR7","unstructured":"Blumberg, A.J., Lesnick, M.: Universality of the homotopy interleaving distance (2017). arXiv:1705.01690"},{"issue":"6","key":"104_CR8","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1007\/s10208-013-9177-5","volume":"13","author":"AJ Blumberg","year":"2013","unstructured":"Blumberg, A.J., Mandell, M.A.: Quantitative homotopy theory in topological data analysis. Found. Comput. Math. 13(6), 885\u2013911 (2013)","journal-title":"Found. Comput. Math."},{"issue":"1\u20132","key":"104_CR9","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s00200-014-0247-y","volume":"26","author":"MB Botnan","year":"2015","unstructured":"Botnan, M.B., Spreemann, G.: Approximating persistent homology in Euclidean space through collapses. Appl. Algebra Eng. Commun. Comput. 26(1\u20132), 73\u2013101 (2015)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"3","key":"104_CR10","doi-asserted-by":"publisher","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."},{"key":"104_CR11","volume-title":"A Course in Metric Geometry Graduate Studies in Mathematics","author":"D Burago","year":"2001","unstructured":"Burago, D., Burago, Yu., Ivanov, S.: A Course in Metric Geometry Graduate Studies in Mathematics, vol. 33. American Mathematical Society, Providence (2001)"},{"issue":"2","key":"104_CR12","doi-asserted-by":"publisher","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(2), 255\u2013308 (2009)","journal-title":"Bull. Am. Math. Soc."},{"key":"104_CR13","unstructured":"Cavanna, N.J., Jahanseir, M., Sheehy, D.R.: A geometric perspective on sparse filtrations (2015). arXiv:1506.03797"},{"issue":"5","key":"104_CR14","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1111\/j.1467-8659.2009.01516.x","volume":"28","author":"F Chazal","year":"2009","unstructured":"Chazal, F., Cohen-Steiner, D., Guibas, L.J., M\u00e9moli, F., Oudot, S.Y.: Gromov\u2013Hausdorff stable signatures for shapes using persistence. Comput. Gr. Forum 28(5), 1393\u20131403 (2009)","journal-title":"Comput. Gr. Forum"},{"key":"104_CR15","series-title":"SpringerBriefs in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-42545-0","volume-title":"The Structure and Stability of Persistence Modules","author":"F Chazal","year":"2016","unstructured":"Chazal, F., De Silva, V., Glisse, M., Oudot, S.: The Structure and Stability of Persistence Modules. SpringerBriefs in Mathematics. Springer, Cham (2016)"},{"issue":"1","key":"104_CR16","doi-asserted-by":"publisher","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"},{"key":"104_CR17","unstructured":"Chowdhury, S., M\u00e9moli, F.: Persistent homology of asymmetric networks: an approach based on Dowker filtrations (2016). arXiv:1608.05432"},{"key":"104_CR18","doi-asserted-by":"crossref","unstructured":"Dey, T.K., Fan, F., Wang, Y.: Computing topological persistence for simplicial maps. In: Proceedings of the 30th Annual Symposium on Computational Geometry (SoCG\u201914), pp. 345\u2013354. ACM, New York (2014)","DOI":"10.1145\/2582112.2582165"},{"key":"104_CR19","doi-asserted-by":"crossref","unstructured":"Dey, T.K., M\u00e9moli, F., Wang, Y.: Multiscale mapper: topological summarization via codomain covers. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201916), pp. 997\u20131013. SIAM, Philadelphia (2016)","DOI":"10.1137\/1.9781611974331.ch71"},{"key":"104_CR20","unstructured":"Dey, T.K., Shi, D., Wang, Y.: SimBa: An efficient tool for approximating rips-filtration persistence via simplicial batch-collapse (2016). arXiv:1609.07517"},{"key":"104_CR21","volume-title":"Computational Topology: An Introduction","author":"H Edelsbrunner","year":"2010","unstructured":"Edelsbrunner, H., Harer, J.L.: Computational Topology: An Introduction. American Mathematical Society, Providence (2010)"},{"key":"104_CR22","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 454\u2013463. IEEE, Los Alamitos (2000)"},{"key":"104_CR23","unstructured":"Edelsbrunner, H., Morozov, D.: Persistent homology: theory and practice. Technical report, Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley (2012)"},{"key":"104_CR24","volume-title":"Algebraic Topology","author":"A Hatcher","year":"2002","unstructured":"Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)"},{"key":"104_CR25","first-page":"175","volume-title":"Prospects in Topology Annals of Mathematics Studies","author":"J-C Hausmann","year":"1995","unstructured":"Hausmann, J.-C.: On the Vietoris\u2013Rips complexes and a cohomology theory for metric spaces. In: Quinn, F. (ed.) Prospects in Topology Annals of Mathematics Studies, vol. 138, pp. 175\u2013188. Princeton University Press, Princeton (1995)"},{"key":"104_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1007\/978-3-642-45030-3_62","volume-title":"International Symposium on Algorithms and Computation","author":"M Kerber","year":"2013","unstructured":"Kerber, M., Sharathkumar, R.: Approximate \u010cech complex in low and high dimensions. International Symposium on Algorithms and Computation. Lecture Notes in Computer Science, vol. 8283, pp. 666\u2013676. Springer, Heidelberg (2013)"},{"issue":"6","key":"104_CR27","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1007\/PL00000526","volume":"77","author":"J Latschev","year":"2001","unstructured":"Latschev, J.: Vietoris\u2013Rips complexes of metric spaces near a closed Riemannian manifold. Arch. Math. 77(6), 522\u2013528 (2001)","journal-title":"Arch. Math."},{"key":"104_CR28","series-title":"American Mathematical Society Colloquium Publications","doi-asserted-by":"crossref","DOI":"10.1090\/coll\/027","volume-title":"Algebraic Topology","author":"S Lefschetz","year":"1942","unstructured":"Lefschetz, S.: Algebraic Topology. American Mathematical Society Colloquium Publications, vol. 27. American Mathematical Society, New York (1942)"},{"issue":"3","key":"104_CR29","doi-asserted-by":"publisher","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":"2","key":"104_CR30","first-page":"37","volume":"3","author":"J Matou\u0161ek","year":"2008","unstructured":"Matou\u0161ek, J.: LC reductions yield isomorphic simplicial complexes. Contrib. Discrete Math. 3(2), 37\u201339 (2008)","journal-title":"Contrib. Discrete Math."},{"key":"104_CR31","unstructured":"M\u00e9moli, F.: A distance between filtered spaces via tripods (2017). arXiv:1704.03965"},{"key":"104_CR32","unstructured":"Morozov, D., Beketayev, K., Weber, G.: Interleaving distance between merge trees. Presented at TopoInVis\u201913. https:\/\/www.sci.utah.edu\/topoinvis13.html"},{"key":"104_CR33","doi-asserted-by":"publisher","DOI":"10.1201\/9780429493911","volume-title":"Elements of Algebraic Topology","author":"JR Munkres","year":"2018","unstructured":"Munkres, J.R.: Elements of Algebraic Topology. CRC Press, Boca Raton (2018)"},{"issue":"4","key":"104_CR34","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1007\/s00454-013-9513-1","volume":"49","author":"DR Sheehy","year":"2013","unstructured":"Sheehy, D.R.: Linear-size approximations to the Vietoris\u2013Rips filtration. Discrete Comput. Geom. 49(4), 778\u2013796 (2013)","journal-title":"Discrete Comput. Geom."},{"key":"104_CR35","doi-asserted-by":"crossref","unstructured":"Zomorodian, A.: The tidy set: a minimal simplicial set for computing homology of clique complexes. In: Proceedings of the 26th Annual Symposium on Computational Geometry (SoCG\u201910), pp. 257\u2013266. ACM, New York (2010)","DOI":"10.1145\/1810959.1811004"},{"issue":"2","key":"104_CR36","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s00454-004-1146-y","volume":"33","author":"A Zomorodian","year":"2005","unstructured":"Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33(2), 249\u2013274 (2005)","journal-title":"Discrete Comput. Geom."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00104-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-019-00104-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00104-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T19:56:43Z","timestamp":1612900603000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-019-00104-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,30]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["104"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00104-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,30]]},"assertion":[{"value":"12 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 April 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 May 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}