{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:12:47Z","timestamp":1776845567724,"version":"3.51.2"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2011,9]]},"DOI":"10.1007\/s00454-010-9303-y","type":"journal-article","created":{"date-parts":[[2010,10,14]],"date-time":"2010-10-14T07:27:25Z","timestamp":1287041245000},"page":"361-388","source":"Crossref","is-referenced-by-count":29,"title":["Coreduction Homology Algorithm for Regular CW-Complexes"],"prefix":"10.1007","volume":"46","author":[{"given":"Pawe\u0142","family":"D\u0142otko","sequence":"first","affiliation":[]},{"given":"Tomasz","family":"Kaczynski","sequence":"additional","affiliation":[]},{"given":"Marian","family":"Mrozek","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Wanner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,10,14]]},"reference":[{"key":"9303_CR1","volume-title":"Random Fields and Geometry","author":"R.J. Adler","year":"2007","unstructured":"Adler, R.J., Taylor, J.E.: Random Fields and Geometry. Springer, New York (2007)"},{"key":"9303_CR2","first-page":"1","volume-title":"Mathematical Methods and Models in Phase Transitions","author":"D. Bl\u00f6mker","year":"2005","unstructured":"Bl\u00f6mker, D., Maier-Paape, S., Wanner, T.: Phase separation in stochastic Cahn-Hilliard models. In: Miranville, A. (ed.) Mathematical Methods and Models in Phase Transitions, pp. 1\u201341. Nova Science, New York (2005)"},{"key":"9303_CR3","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0647-7","volume-title":"Topology and Geometry","author":"G.E. Bredon","year":"1997","unstructured":"Bredon, G.E.: Topology and Geometry. Graduate Texts in Mathematics, vol.\u00a0139. Springer, New York (1997)"},{"key":"9303_CR4","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1090\/S1079-6762-07-00175-8","volume":"13","author":"S. Day","year":"2007","unstructured":"Day, S., Kalies, W.D., Mischaikow, K., Wanner, T.: Probabilistic and numerical validation of homology computations for nodal domains. Electron. Res. Announc. Am. Math. Soc. 13, 60\u201373 (2007)","journal-title":"Electron. Res. Announc. Am. Math. Soc."},{"issue":"4","key":"9303_CR5","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1137\/080735722","volume":"7","author":"S. Day","year":"2009","unstructured":"Day, S., Kalies, W.D., Wanner, T.: Verified homology computations for nodal domains. SIAM J. Multiscale Model. Simul. 7(4), 1695\u20131726 (2009)","journal-title":"SIAM J. Multiscale Model. Simul."},{"key":"9303_CR6","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1145\/160985.161140","volume-title":"SCG \u201993: Proceedings of the Ninth Annual Symposium on Computational Geometry","author":"C.J.A. Delfinado","year":"1993","unstructured":"Delfinado, C.J.A., Edelsbrunner, H.: An incremental algorithm for Betti numbers of simplicial complexes. In: SCG \u201993: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp.\u00a0232\u2013239. ACM, New York (1993)"},{"key":"9303_CR7","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/978-3-662-05148-1_10","volume-title":"Algebra, Geometry, and Software Systems","author":"J.-G. Dumas","year":"2003","unstructured":"Dumas, J.-G., Heckenbach, F., Saunders, D., Welker, V.: Computing simplicial homology based on efficient Smith normal form algorithms. In: Algebra, Geometry, and Software Systems, pp. 177\u2013206. Springer, Berlin (2003)"},{"issue":"4","key":"9303_CR8","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H. Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28(4), 511\u2013533 (2002)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"9303_CR9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/PL00009218","volume":"21","author":"J. Friedman","year":"1998","unstructured":"Friedman, J.: Computing Betti numbers via combinatorial Laplacians. Algorithmica 21(4), 331\u2013346 (1998)","journal-title":"Algorithmica"},{"issue":"3","key":"9303_CR10","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/j.actamat.2004.10.022","volume":"53","author":"M. Gameiro","year":"2005","unstructured":"Gameiro, M., Mischaikow, K., Wanner, T.: Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation. Acta Mater. 53(3), 693\u2013704 (2005)","journal-title":"Acta Mater."},{"key":"9303_CR11","unstructured":"Juda, M., Mrozek, M.: \u21242-homology of weak 2-pseudomanifolds may be computed in O(n \u03b1(n)) time. Preprint, Jagiellonian University, Computer Science Department (2010). Available online at http:\/\/www.ii.uj.edu.pl\/~mrozek\/papers\/homology-of-2-manifolds-15.pdf"},{"issue":"2","key":"9303_CR12","doi-asserted-by":"crossref","first-page":"233","DOI":"10.4310\/HHA.2003.v5.n2.a8","volume":"5","author":"T. Kaczynski","year":"2003","unstructured":"Kaczynski, T., Mischaikow, K., Mrozek, M.: Computing homology. Homology Homotopy Appl. 5(2), 233\u2013256 (2003)","journal-title":"Homology Homotopy Appl."},{"key":"9303_CR13","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/b97315","volume-title":"Computational Homology","author":"T. Kaczynski","year":"2004","unstructured":"Kaczynski, T., Mischaikow, K., Mrozek, M.: Computational Homology. Applied Mathematical Sciences, vol.\u00a0157. Springer, New York (2004)"},{"issue":"4","key":"9303_CR14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0898-1221(97)00289-7","volume":"35","author":"T. Kaczynski","year":"1998","unstructured":"Kaczynski, T., Mrozek, M., \u015alusarek, M.: Homology computation by reduction of chain complexes. Comput. Math. Appl. 35(4), 59\u201370 (1998)","journal-title":"Comput. Math. Appl."},{"key":"9303_CR15","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4939-9063-4","volume-title":"A Basic Course in Algebraic Topology","author":"W.S. Massey","year":"1991","unstructured":"Massey, W.S.: A Basic Course in Algebraic Topology. Graduate Texts in Mathematics, vol.\u00a0127. Springer, New York (1991)"},{"issue":"3","key":"9303_CR16","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1214\/105051607000000050","volume":"17","author":"K. Mischaikow","year":"2007","unstructured":"Mischaikow, K., Wanner, T.: Probabilistic validation of homology computations for nodal domains. Ann. Appl. Probab. 17(3), 980\u20131018 (2007)","journal-title":"Ann. Appl. Probab."},{"issue":"3","key":"9303_CR17","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1214\/09-AAP652","volume":"20","author":"K. Mischaikow","year":"2010","unstructured":"Mischaikow, K., Wanner, T.: Topology-guided sampling of nonhomogeneous random processes. Ann. Appl. Probab. 20(3), 1068\u20131097 (2010)","journal-title":"Ann. Appl. Probab."},{"issue":"3","key":"9303_CR18","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1007\/s00454-010-9255-2","volume":"44","author":"M. Mrozek","year":"2010","unstructured":"Mrozek, M.: Cech type approach to computing homology of maps. Discrete Comput. Geom. 44(3), 546\u2013576 (2010)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"9303_CR19","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s00454-008-9073-y","volume":"41","author":"M. Mrozek","year":"2009","unstructured":"Mrozek, M., Batko, B.: Coreduction homology algorithm. Discrete Comput. Geom. 41(1), 96\u2013118 (2009)","journal-title":"Discrete Comput. Geom."},{"issue":"11","key":"9303_CR20","doi-asserted-by":"crossref","first-page":"2395","DOI":"10.1016\/j.camwa.2007.08.044","volume":"55","author":"M. Mrozek","year":"2008","unstructured":"Mrozek, M., Pilarczyk, P., \u017belazna, N.: Homology algorithm based on acyclic subspace. Comput. Math. Appl. 55(11), 2395\u20132412 (2008)","journal-title":"Comput. Math. Appl."},{"key":"9303_CR21","unstructured":"Mrozek, M., Wanner, T.: Coreduction homology algorithm for inclusions and persistent homology. Comput. Math. Appl. (in press)"},{"key":"9303_CR22","volume-title":"Elements of Algebraic Topology","author":"J.R. Munkres","year":"1984","unstructured":"Munkres, J.R.: Elements of Algebraic Topology. Addison-Wesley, Menlo Park (1984)"},{"issue":"7","key":"9303_CR23","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1016\/j.imavis.2008.06.009","volume":"27","author":"S. Peltier","year":"2009","unstructured":"Peltier, S., Ion, A., Kropatsch, W., Damiand, G., Haxhimusa, Y.: Directly computing the generators of image homology using graph pyramids. Image Vis. Comput. 27(7), 846\u2013853 (2009)","journal-title":"Image Vis. Comput."},{"key":"9303_CR24","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1145\/236869.237084","volume-title":"Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, ISSAC \u201996","author":"A. Storjohann","year":"1996","unstructured":"Storjohann, A.: Near optimal algorithms for computing smith normal forms of integer matrices. In: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, ISSAC \u201996, pp.\u00a0267\u2013274. ACM, New York (1996)"},{"issue":"1","key":"9303_CR25","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.actamat.2009.08.061","volume":"58","author":"T. Wanner","year":"2010","unstructured":"Wanner, T., Fuller Jr., E.R., Saylor, D.M.: Homological characterization of microstructure response fields in polycrystals. Acta Mater. 58(1), 102\u2013110 (2010)","journal-title":"Acta Mater."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s00454-010-9303-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T21:55:40Z","timestamp":1591998940000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-010-9303-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,14]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["9303"],"URL":"https:\/\/doi.org\/10.1007\/s00454-010-9303-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,14]]}}}