[{"publisher":"Elsevier","intvolume":"       138","abstract":[{"lang":"eng","text":"Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available."}],"has_accepted_license":"1","corr_author":"1","quality_controlled":"1","ddc":["500"],"publication":"Journal of Symbolic Computation","OA_place":"publisher","date_published":"2026-06-23T00:00:00Z","PlanS_conform":"1","arxiv":1,"article_processing_charge":"No","acknowledgement":"This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR, under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also like to thank Lars M Salbu for fruitful discussions regarding the operators from Definition 4.1 and their relation with the order relations introduced in Definition 3.2.","date_updated":"2026-07-13T12:00:07Z","author":[{"last_name":"Gonzalez-Diaz","first_name":"Rocio","full_name":"Gonzalez-Diaz, Rocio"},{"id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","orcid":"0000-0003-2449-1433","last_name":"Soriano Trigueros","full_name":"Soriano Trigueros, Manuel","first_name":"Manuel"},{"last_name":"Torras-Casas","full_name":"Torras-Casas, Alvaro","first_name":"Alvaro"}],"dataavailabilitystatement":"The code used for the computational experiments is available in https://github.com/Cimagroup/IBloFunMatch","year":"2026","main_file_link":[{"url":"https://doi.org/10.1016/j.jsc.2026.102598","open_access":"1"}],"department":[{"_id":"HeEd"}],"volume":138,"type":"journal_article","scopus_import":"1","doi":"10.1016/j.jsc.2026.102598","article_type":"original","language":[{"iso":"eng"}],"researchdata_availability":"yes","oa":1,"external_id":{"arxiv":["2006.11100"]},"month":"06","status":"public","das_tickbox":"1","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"date_created":"2026-07-13T09:43:38Z","mathsc":["55N31","16G20"],"supplementarymaterial":"no","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Persistence module","Persistence map","Persistent homology"],"citation":{"ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138. doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>.","mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>.","short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic Computation 138 (2026).","ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>, vol. 138. Elsevier, 2026.","apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>"},"day":"23","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa_version":"Published Version","OA_type":"hybrid","publication_status":"epub_ahead","_id":"22291","title":"Additive partial matchings induced by persistence maps","fulldoi":"https://doi.org/10.1016/j.jsc.2026.102598","article_number":"102598"},{"_id":"4060","title":"Tetrahedrizing point sets in three dimensions","fulldoi":"https://doi.org/10.1016/S0747-7171(08)80068-5","oa_version":"Published Version","publication_status":"published","day":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347.","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>.","apa":"Edelsbrunner, H., Preparata, F., &#38; West, D. (1990). Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990.","ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. 1990;10(3-4):335-347. doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>.","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347."},"status":"public","publist_id":"2061","publication_identifier":{"eissn":["1095-855X"],"issn":["0747-7171"]},"date_created":"2018-12-11T12:06:42Z","month":"01","issue":"3-4","oa":1,"page":"335 - 347","doi":"10.1016/S0747-7171(08)80068-5","article_type":"original","language":[{"iso":"eng"}],"volume":10,"scopus_import":"1","type":"journal_article","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Preparata","full_name":"Preparata, Franco","first_name":"Franco"},{"last_name":"West","first_name":"Douglas","full_name":"West, Douglas"}],"date_updated":"2022-02-23T10:10:35Z","year":"1990","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub","open_access":"1"}],"article_processing_charge":"No","acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322.","extern":"1","publication":"Journal of Symbolic Computation","date_published":"1990-01-01T00:00:00Z","quality_controlled":"1","abstract":[{"lang":"eng","text":"This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra."}],"publisher":"Elsevier","intvolume":"        10"},{"article_processing_charge":"No","extern":"1","type":"journal_article","scopus_import":"1","volume":2,"author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"first_name":"Roman","full_name":"Waupotitsch, Roman","last_name":"Waupotitsch"}],"date_updated":"2022-02-01T11:22:59Z","year":"1986","abstract":[{"text":"Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time.","lang":"eng"}],"intvolume":"         2","publisher":"Elsevier","publication":"Journal of Symbolic Computation","date_published":"1986-01-01T00:00:00Z","quality_controlled":"1","day":"01","citation":{"ieee":"H. Edelsbrunner and R. Waupotitsch, “Computing a ham-sandwich cut in two dimensions,” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2. Elsevier, pp. 171–178, 1986.","apa":"Edelsbrunner, H., &#38; Waupotitsch, R. (1986). Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>","mla":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2, Elsevier, 1986, pp. 171–78, doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>.","short":"H. Edelsbrunner, R. Waupotitsch, Journal of Symbolic Computation 2 (1986) 171–178.","ista":"Edelsbrunner H, Waupotitsch R. 1986. Computing a ham-sandwich cut in two dimensions. Journal of Symbolic Computation. 2(2), 171–178.","chicago":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>.","ama":"Edelsbrunner H, Waupotitsch R. Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. 1986;2(2):171-178. doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>"},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4106","fulldoi":"https://doi.org/10.1016/S0747-7171(86)80020-7","title":"Computing a ham-sandwich cut in two dimensions","publication_status":"published","oa_version":"None","page":"171 - 178","doi":"10.1016/S0747-7171(86)80020-7","article_type":"original","language":[{"iso":"eng"}],"status":"public","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"date_created":"2018-12-11T12:06:58Z","publist_id":"2018","issue":"2","month":"01"},{"publist_id":"2004","date_created":"2018-12-11T12:07:03Z","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"status":"public","issue":"1","month":"03","page":"47 - 56","oa":1,"article_type":"original","language":[{"iso":"eng"}],"doi":"10.1016/S0747-7171(85)80028-6","fulldoi":"https://doi.org/10.1016/S0747-7171(85)80028-6","title":"Optimal solutions for a class of point retrieval problems","_id":"4120","publication_status":"published","oa_version":"Published Version","day":"01","citation":{"ista":"Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 47–56.","chicago":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>. Elsevier, 1985. <a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">https://doi.org/10.1016/S0747-7171(85)80028-6</a>.","ama":"Chazelle B, Edelsbrunner H. Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. 1985;1(1):47-56. doi:<a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">10.1016/S0747-7171(85)80028-6</a>","ieee":"B. Chazelle and H. Edelsbrunner, “Optimal solutions for a class of point retrieval problems,” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1. Elsevier, pp. 47–56, 1985.","apa":"Chazelle, B., &#38; Edelsbrunner, H. (1985). Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">https://doi.org/10.1016/S0747-7171(85)80028-6</a>","short":"B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56.","mla":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1, Elsevier, 1985, pp. 47–56, doi:<a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">10.1016/S0747-7171(85)80028-6</a>."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_published":"1985-03-01T00:00:00Z","publication":"Journal of Symbolic Computation","quality_controlled":"1","abstract":[{"lang":"eng","text":"Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution."}],"intvolume":"         1","publisher":"Elsevier","type":"journal_article","volume":1,"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub","open_access":"1"}],"year":"1985","author":[{"full_name":"Chazelle, Bernard","first_name":"Bernard","last_name":"Chazelle"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"}],"date_updated":"2022-01-31T09:20:18Z","article_processing_charge":"No","acknowledgement":"The first author was supported i~1 part by NSF grants MCS 83-03925 and the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-g3-K-0146 and ARPA Order No. 4786.","extern":"1"}]