{"id":"https://openalex.org/W2065419861","doi":"https://doi.org/10.1007/s10589-012-9458-y","title":"Branch and cut algorithms for detecting critical nodes in undirected graphs","display_name":"Branch and cut algorithms for detecting critical nodes in undirected graphs","publication_year":2012,"publication_date":"2012-02-08","ids":{"openalex":"https://openalex.org/W2065419861","doi":"https://doi.org/10.1007/s10589-012-9458-y","mag":"2065419861"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-012-9458-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-012-9458-y","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2318/131733","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086066603","display_name":"Marco Di Summa","orcid":"https://orcid.org/0000-0001-7223-0380"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Di\u00a0Summa","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, Via Trieste, 63, 35121, Padova, Italy","Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, Padova, Italy 35121#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, Via Trieste, 63, 35121, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, Padova, Italy 35121#TAB#","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038879415","display_name":"Andrea Grosso","orcid":"https://orcid.org/0000-0002-9926-2443"},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Grosso","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 degli Studi di Torino, Corso Svizzera, 185, 10149, Torino, Italy","Dipartimento di Informatica, Universit\u00e0 degli Studi di Torino, Torino, Italy 10149#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Torino, Corso Svizzera, 185, 10149, Torino, Italy","institution_ids":["https://openalex.org/I55143463"]},{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Torino, Torino, Italy 10149#TAB#","institution_ids":["https://openalex.org/I55143463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050902529","display_name":"Marco Locatelli","orcid":"https://orcid.org/0000-0001-7138-8653"},"institutions":[{"id":"https://openalex.org/I124601658","display_name":"University of Parma","ror":"https://ror.org/02k7wn190","country_code":"IT","type":"education","lineage":["https://openalex.org/I124601658"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Locatelli","raw_affiliation_strings":["Dipartimento di Ingegneria Informatica, Universit\u00e0 di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy","Dipartimento di Ingegneria Informatica, Universit\u00e0 di Parma, Parma, Italy 43124#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Informatica, Universit\u00e0 di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy","institution_ids":["https://openalex.org/I124601658"]},{"raw_affiliation_string":"Dipartimento di Ingegneria Informatica, Universit\u00e0 di Parma, Parma, Italy 43124#TAB#","institution_ids":["https://openalex.org/I124601658"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086066603"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.9426,"has_fulltext":true,"cited_by_count":119,"citation_normalized_percentile":{"value":0.97441997,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"53","issue":"3","first_page":"649","last_page":"680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.996399998664856,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.996399998664856,"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/T10847","display_name":"Advanced Optical Network Technologies","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7326393127441406},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.618395209312439},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5488616824150085},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5483468770980835},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5092257261276245},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4956306219100952},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.49395400285720825},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.46051517128944397},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4592544734477997},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4435203969478607},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4285876750946045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3814549148082733},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3734850287437439},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3413425385951996}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7326393127441406},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.618395209312439},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5488616824150085},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5483468770980835},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5092257261276245},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4956306219100952},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.49395400285720825},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.46051517128944397},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4592544734477997},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4435203969478607},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4285876750946045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3814549148082733},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3734850287437439},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3413425385951996},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10589-012-9458-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-012-9458-y","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:iris.unito.it:2318/131733","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/131733","pdf_url":"http://hdl.handle.net/2318/131733","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.416.5550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.416.5550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2011/07/3107.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:coopap:v:53:y:2012:i:3:p:649-680","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10589-012-9458-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:www.research.unipd.it:11577/2525416","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/2525416","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unito.it:2318/131733","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/131733","pdf_url":"http://hdl.handle.net/2318/131733","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065419861.pdf","grobid_xml":"https://content.openalex.org/works/W2065419861.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W396542372","https://openalex.org/W972994255","https://openalex.org/W1557310162","https://openalex.org/W1564910180","https://openalex.org/W1567877685","https://openalex.org/W1966279959","https://openalex.org/W1978797771","https://openalex.org/W1996684664","https://openalex.org/W1999613943","https://openalex.org/W2027109023","https://openalex.org/W2034304357","https://openalex.org/W2045640143","https://openalex.org/W2049143039","https://openalex.org/W2063190731","https://openalex.org/W2076535438","https://openalex.org/W2105880662","https://openalex.org/W2121035174","https://openalex.org/W2123785786","https://openalex.org/W2133494553","https://openalex.org/W2503371504","https://openalex.org/W2998757566","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4252122881","https://openalex.org/W134055995","https://openalex.org/W2009796757","https://openalex.org/W4302819359","https://openalex.org/W1973873435","https://openalex.org/W4244487479","https://openalex.org/W1963627056","https://openalex.org/W2769220156","https://openalex.org/W1981191225","https://openalex.org/W4232431455"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-15T08:27:34.491423","created_date":"2025-10-10T00:00:00"}