{"id":"https://openalex.org/W7165372838","doi":"https://doi.org/10.1186/s13015-026-00300-5","title":"Extension of partial atom-to-atom maps: uniqueness and algorithms","display_name":"Extension of partial atom-to-atom maps: uniqueness and algorithms","publication_year":2026,"publication_date":"2026-06-19","ids":{"openalex":"https://openalex.org/W7165372838","doi":"https://doi.org/10.1186/s13015-026-00300-5","pmid":"https://pubmed.ncbi.nlm.nih.gov/42321843"},"language":"en","primary_location":{"id":"doi:10.1186/s13015-026-00300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13015-026-00300-5","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13015-026-00300-5.pdf","source":{"id":"https://openalex.org/S205663195","display_name":"Algorithms for Molecular Biology","issn_l":"1748-7188","issn":["1748-7188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms for Molecular Biology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1186/s13015-026-00300-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057152287","display_name":"Marcos E. Gonz\u00e1lez Laffitte","orcid":"https://orcid.org/0009-0008-2307-595X"},"institutions":[{"id":"https://openalex.org/I40900055","display_name":"Telstra (Australia)","ror":"https://ror.org/04g047260","country_code":"AU","type":"company","lineage":["https://openalex.org/I40900055"]},{"id":"https://openalex.org/I4401726909","display_name":"Center for Scalable Data Analytics and Artificial Intelligence","ror":"https://ror.org/01t4ttr56","country_code":"DE","type":"education","lineage":["https://openalex.org/I4401726909","https://openalex.org/I78650965","https://openalex.org/I926574661"]},{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["AU","DE"],"is_corresponding":true,"raw_author_name":"Marcos E. Gonz\u00e1lez Laffitte","raw_affiliation_strings":["Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. marcos@bioinf.uni-leipzig.de","Center for Scalable Data Analytics and Artificial Intelligence Dresden-Leipzig (ScaDS.AI), Leipzig University, Humboldtstrasse 25, 04105, Leipzig, Saxony, Germany. marcos@bioinf.uni-leipzig.de"],"raw_orcid":"https://orcid.org/0009-0008-2307-595X","affiliations":[{"raw_affiliation_string":"Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. marcos@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I40900055","https://openalex.org/I926574661"]},{"raw_affiliation_string":"Center for Scalable Data Analytics and Artificial Intelligence Dresden-Leipzig (ScaDS.AI), Leipzig University, Humboldtstrasse 25, 04105, Leipzig, Saxony, Germany. marcos@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I4401726909","https://openalex.org/I926574661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045412670","display_name":"Tieu-Long Phan","orcid":"https://orcid.org/0000-0002-3532-2064"},"institutions":[{"id":"https://openalex.org/I177969490","display_name":"University of Southern Denmark","ror":"https://ror.org/03yrrjy16","country_code":"DK","type":"education","lineage":["https://openalex.org/I177969490"]},{"id":"https://openalex.org/I40900055","display_name":"Telstra (Australia)","ror":"https://ror.org/04g047260","country_code":"AU","type":"company","lineage":["https://openalex.org/I40900055"]}],"countries":["AU","DK"],"is_corresponding":true,"raw_author_name":"Tieu-Long Phan","raw_affiliation_strings":["Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. tieu@bioinf.uni-leipzig.de","Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Funen, Odense, Denmark. tieu@bioinf.uni-leipzig.de"],"raw_orcid":"https://orcid.org/0000-0002-3532-2064","affiliations":[{"raw_affiliation_string":"Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. tieu@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I40900055"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Funen, Odense, Denmark. tieu@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I177969490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016104736","display_name":"Peter F. Stadler","orcid":"https://orcid.org/0000-0002-5016-5191"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I177969490","display_name":"University of Southern Denmark","ror":"https://ror.org/03yrrjy16","country_code":"DK","type":"education","lineage":["https://openalex.org/I177969490"]},{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]},{"id":"https://openalex.org/I40900055","display_name":"Telstra (Australia)","ror":"https://ror.org/04g047260","country_code":"AU","type":"company","lineage":["https://openalex.org/I40900055"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4401726909","display_name":"Center for Scalable Data Analytics and Artificial Intelligence","ror":"https://ror.org/01t4ttr56","country_code":"DE","type":"education","lineage":["https://openalex.org/I4401726909","https://openalex.org/I78650965","https://openalex.org/I926574661"]},{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["AT","AU","CO","DE","DK","US"],"is_corresponding":true,"raw_author_name":"Peter F. Stadler","raw_affiliation_strings":["Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","Center for Scalable Data Analytics and Artificial Intelligence Dresden-Leipzig (ScaDS.AI), Leipzig University, Humboldtstrasse 25, 04105, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Funen, Odense, Denmark. studla@bioinf.uni-leipzig.de","Facultad de Ciencias, Universidad National de Colombia, Carrera 45, 111321, Bogot\u00e1, Cundinamarca, Colombia. studla@bioinf.uni-leipzig.de","Institute for Theoretical Chemistry, University of Vienna, Waehringer Strasse 17, 1090, Vienna, Austria. studla@bioinf.uni-leipzig.de","Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, New Mexico, 87501, USA. studla@bioinf.uni-leipzig.de"],"raw_orcid":"https://orcid.org/0000-0002-5016-5191","affiliations":[{"raw_affiliation_string":"Bioinformatics Group, Department of Computer Science and Interdisciplinary Center of Bioinformatics, Leipzig University, Haertelstrasse 16-18, 04107, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I40900055"]},{"raw_affiliation_string":"Center for Scalable Data Analytics and Artificial Intelligence Dresden-Leipzig (ScaDS.AI), Leipzig University, Humboldtstrasse 25, 04105, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I4401726909","https://openalex.org/I926574661"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Funen, Odense, Denmark. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I177969490"]},{"raw_affiliation_string":"Facultad de Ciencias, Universidad National de Colombia, Carrera 45, 111321, Bogot\u00e1, Cundinamarca, Colombia. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I36243813"]},{"raw_affiliation_string":"Institute for Theoretical Chemistry, University of Vienna, Waehringer Strasse 17, 1090, Vienna, Austria. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Saxony, Germany. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, New Mexico, 87501, USA. studla@bioinf.uni-leipzig.de","institution_ids":["https://openalex.org/I1308548392"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5016104736","https://openalex.org/A5045412670","https://openalex.org/A5057152287"],"corresponding_institution_ids":["https://openalex.org/I129774422","https://openalex.org/I1308548392","https://openalex.org/I177969490","https://openalex.org/I36243813","https://openalex.org/I40900055","https://openalex.org/I4210091327","https://openalex.org/I4401726909","https://openalex.org/I926574661"],"apc_list":{"value":2290,"currency":"USD","value_usd":2290},"apc_paid":{"value":2290,"currency":"USD","value_usd":2290},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.64496555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.3889000117778778,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.3889000117778778,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10211","display_name":"Computational Drug Discovery Methods","score":0.20890000462532043,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.06199999898672104,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7840999960899353},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6686999797821045},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5335999727249146},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.4578000009059906},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.42399999499320984},{"id":"https://openalex.org/keywords/partial-oxidation","display_name":"Partial oxidation","score":0.420199990272522},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3905999958515167}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7840999960899353},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6686999797821045},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5335999727249146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48919999599456787},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.4578000009059906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4487999975681305},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C110686534","wikidata":"https://www.wikidata.org/wiki/Q451467","display_name":"Partial oxidation","level":3,"score":0.420199990272522},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3066999912261963},{"id":"https://openalex.org/C177801218","wikidata":"https://www.wikidata.org/wiki/Q36534","display_name":"Chemical reaction","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C12892243","wikidata":"https://www.wikidata.org/wiki/Q901147","display_name":"Partial charge","level":3,"score":0.2937000095844269},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.2535000145435333}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1186/s13015-026-00300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13015-026-00300-5","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13015-026-00300-5.pdf","source":{"id":"https://openalex.org/S205663195","display_name":"Algorithms for Molecular Biology","issn_l":"1748-7188","issn":["1748-7188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms for Molecular Biology","raw_type":"journal-article"},{"id":"pmid:42321843","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42321843","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms for molecular biology : AMB","raw_type":null},{"id":"pmh:oai:sdu.dk:openaire/fc6b8b1d-3d9b-415d-8920-ab350cd1ef4d","is_oa":true,"landing_page_url":"https://portal.findresearcher.sdu.dk/da/publications/fc6b8b1d-3d9b-415d-8920-ab350cd1ef4d","pdf_url":null,"source":{"id":"https://openalex.org/S4306400423","display_name":"University of Southern Denmark Research Portal (University of Southern Denmark)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177969490","host_organization_name":"University of Southern Denmark","host_organization_lineage":["https://openalex.org/I177969490"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Laffitte, M E G, Phan, T L & Stadler, P F 2026, 'Extension of partial atom-to-atom maps : uniqueness and algorithms', Algorithms for Molecular Biology, vol. 21, no. 1, 10. https://doi.org/10.1186/s13015-026-00300-5","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e1c9d255392c41d08ab4a61c5788d722","is_oa":false,"landing_page_url":"https://doaj.org/article/e1c9d255392c41d08ab4a61c5788d722","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms for Molecular Biology, Vol 21, Iss 1 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13282873","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13282873/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms Mol Biol","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1186/s13015-026-00300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13015-026-00300-5","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13015-026-00300-5.pdf","source":{"id":"https://openalex.org/S205663195","display_name":"Algorithms for Molecular Biology","issn_l":"1748-7188","issn":["1748-7188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms for Molecular Biology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165372838.pdf","grobid_xml":"https://content.openalex.org/works/W7165372838.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W29374554","https://openalex.org/W1462785842","https://openalex.org/W1512007370","https://openalex.org/W1848248203","https://openalex.org/W1973896848","https://openalex.org/W1974672137","https://openalex.org/W1982870104","https://openalex.org/W1995714561","https://openalex.org/W2011018037","https://openalex.org/W2033788780","https://openalex.org/W2072550304","https://openalex.org/W2099701485","https://openalex.org/W2104266030","https://openalex.org/W2117936065","https://openalex.org/W2132022337","https://openalex.org/W2146405302","https://openalex.org/W2147405597","https://openalex.org/W2551217916","https://openalex.org/W2795196889","https://openalex.org/W2952128502","https://openalex.org/W2963912089","https://openalex.org/W3007883572","https://openalex.org/W3208007731","https://openalex.org/W4243010216","https://openalex.org/W4245305983","https://openalex.org/W4255979597","https://openalex.org/W4321440320","https://openalex.org/W4392752197","https://openalex.org/W4400812658","https://openalex.org/W4402704169","https://openalex.org/W4408055419","https://openalex.org/W4411295511","https://openalex.org/W4413522803","https://openalex.org/W6966644540","https://openalex.org/W7106141426"],"related_works":[],"abstract_inverted_index":{"Chemical":[0],"reaction":[1,119,153,199],"databases":[2],"typically":[3],"report":[4],"the":[5,24,48,70,95,109,118,123,138,142,146,158,171,198],"molecular":[6],"structures":[7],"of":[8,26,50,140,151,173,235],"reactant":[9,27,96],"and":[10,28,47,82,97,175,191],"product":[11,29,98],"compounds,":[12],"as":[13,15],"well":[14],"their":[16,221],"stoichiometry,":[17],"but":[18],"lack":[19],"information,":[20],"in":[21,44,54,209],"particular,":[22],"on":[23],"correspondence":[25],"atoms.":[30],"These":[31],"atom-to-atom":[32],"maps":[33],"(AAM),":[34],"however,":[35],"are":[36,204,214],"crucial":[37],"for":[38,103,244],"applications":[39],"including":[40],"chemical":[41],"synthesis":[42],"planning":[43],"organic":[45],"chemistry":[46],"analysis":[49],"isotope":[51],"labeling":[52],"experiments":[53],"modern":[55],"metabolomics.":[56],"AAMs":[57,75,196,208],"therefore":[58],"need":[59],"to":[60,107,137,145,169,206],"be":[61,85,181,224],"reconstructed":[62],"computationally.":[63],"This":[64,134],"situation":[65],"is":[66,106,154],"aggravated,":[67],"furthermore,":[68],"by":[69,79,88,94,157,226,240],"fact":[71],"that":[72,129,185],"chemically":[73],"correct":[74],"are,":[76],"fundamentally,":[77],"determined":[78],"quantum-mechanical":[80],"phenomena":[81],"thus":[83],"cannot":[84],"reliably":[86],"computed":[87,225],"solving":[89,227],"graph-theoretical":[90],"optimization":[91],"problems":[92],"defined":[93],"structures.":[99],"A":[100],"viable":[101],"solution":[102],"this":[104,219,245],"problem":[105,139],"shift":[108],"focus":[110],"into":[111],"first":[112],"identifying":[113],"a":[114,132,152,165,177,228],"partial":[115,143,178,195,207],"AAM":[116,150,179],"containing":[117],"center,":[120],"i.e.,":[121],"covering":[122],"atoms":[124,213],"incident":[125],"with":[126],"all":[127],"bonds":[128],"change":[130],"during":[131],"reaction.":[133,148],"then":[135],"leads":[136],"extending":[141],"map":[144],"full":[147],"The":[149],"faithfully":[155],"represented":[156,216],"Imaginary":[159],"Transition":[160],"State":[161],"(ITS)":[162],"graph,":[163],"providing":[164],"convenient":[166],"graph-theoretic":[167],"framework":[168],"address":[170],"questions":[172],"when":[174],"how":[176],"can":[180,223],"extended.":[182],"We":[183,238],"show":[184],"an":[186],"unique":[187],"extension":[188,222],"exists":[189],"whenever,":[190],"only":[192],"if,":[193],"these":[194],"cover":[197],"center.":[200],"Moreover,":[201],"uniqueness":[202],"results":[203],"generalized":[205],"situations":[210],"where":[211],"hydrogen":[212],"not":[215],"explicitly.":[217],"In":[218],"case":[220],"constrained":[229],"graph-isomorphism":[230],"search":[231],"between":[232],"specific":[233],"subgraphs":[234],"ITS":[236],"graphs.":[237],"close":[239],"benchmarking":[241],"different":[242],"tools":[243],"task.":[246]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-06-20T00:00:00"}