{"id":"https://openalex.org/W7125947921","doi":"https://doi.org/10.1007/s00493-026-00199-x","title":"Quotient-Convergence of Submodular Setfunctions","display_name":"Quotient-Convergence of Submodular Setfunctions","publication_year":2026,"publication_date":"2026-01-28","ids":{"openalex":"https://openalex.org/W7125947921","doi":"https://doi.org/10.1007/s00493-026-00199-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-026-00199-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-026-00199-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-026-00199-x.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-026-00199-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123623913","display_name":"Krist\u00f3f B\u00e9rczi","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Krist\u00f3f B\u00e9rczi","raw_affiliation_strings":["MTA-ELTE Matroid Optimization Research Group and HUN-REN\u2013ELTE Egerv\u00e1ry Research Group, Department of Operations Research, E\u00f6tv\u00f6s Lor\u00e1nd University, and HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MTA-ELTE Matroid Optimization Research Group and HUN-REN\u2013ELTE Egerv\u00e1ry Research Group, Department of Operations Research, E\u00f6tv\u00f6s Lor\u00e1nd University, and HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012035495","display_name":"M\u00e1rton Borb\u00e9nyi","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"M\u00e1rton Borb\u00e9nyi","raw_affiliation_strings":["Department of Computer Science, E\u00f6tv\u00f6s Lor\u00e1nd University and HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, E\u00f6tv\u00f6s Lor\u00e1nd University and HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067889485","display_name":"L\u00e1szl\u00f3 Lov\u00e1sz","orcid":"https://orcid.org/0000-0002-6242-5894"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 Lov\u00e1sz","raw_affiliation_strings":["HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058606473","display_name":"L\u00e1szl\u00f3 M\u00e1rton T\u00f3th","orcid":"https://orcid.org/0000-0002-6821-8060"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 M\u00e1rton T\u00f3th","raw_affiliation_strings":["HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5123623913"],"corresponding_institution_ids":["https://openalex.org/I106118109","https://openalex.org/I127817813"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17130045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5217999815940857,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5217999815940857,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.062300000339746475,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.04259999841451645,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.871399998664856},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7914000153541565},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7386999726295471},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.5848000049591064},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4964999854564667},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4318999946117401},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.427700012922287},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.42489999532699585},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.41839998960494995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8844000101089478},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.871399998664856},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7914000153541565},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7386999726295471},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6496000289916992},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.5848000049591064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.555400013923645},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.30379998683929443},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-026-00199-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-026-00199-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-026-00199-x.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-026-00199-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-026-00199-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-026-00199-x.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5081458687782288,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4171720266","display_name":null,"funder_award_id":"LP2021-1/2021","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G8859649638","display_name":null,"funder_award_id":"\u00daNKP-23-3","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"}],"funders":[{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"},{"id":"https://openalex.org/F4320326124","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd Tudom\u00e1nyegyetem","ror":"https://ror.org/01jsq2704"},{"id":"https://openalex.org/F4320335908","display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7125947921.pdf","grobid_xml":"https://content.openalex.org/works/W7125947921.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W273178449","https://openalex.org/W2001760341","https://openalex.org/W2017186918","https://openalex.org/W2033810643","https://openalex.org/W2111754130","https://openalex.org/W2134342108","https://openalex.org/W2137365113","https://openalex.org/W2155726088","https://openalex.org/W2165114349","https://openalex.org/W2963336690","https://openalex.org/W4205215823","https://openalex.org/W4231868828","https://openalex.org/W4245588825","https://openalex.org/W4402079994","https://openalex.org/W4417334993"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,59],"introduce":[2],"the":[3,20,31,47,51,97,100],"concept":[4,56],"of":[5,9,22,24,34,53,72,99],"quotient-convergence":[6],"for":[7,19,87],"sequences":[8,41,86],"submodular":[10],"set":[11,64,74,93],"functions,":[12,94],"providing,":[13],"among":[14],"others,":[15],"a":[16,54,70],"new":[17],"framework":[18],"study":[21],"convergence":[23],"matroids":[25],"through":[26],"their":[27],"rank":[28],"functions.":[29],"Extending":[30],"limit":[32],"theory":[33],"bounded":[35,63],"degree":[36],"graphs,":[37],"which":[38],"analyzes":[39],"graph":[40],"via":[42],"neighborhood":[43,55],"sampling,":[44],"we":[45,82],"address":[46],"challenge":[48],"posed":[49],"by":[50,69],"absence":[52],"in":[57],"matroids.":[58],"show":[60],"that":[61,76],"any":[62],"function":[65],"can":[66],"be":[67],"approximated":[68],"sequence":[71],"finite":[73],"functions":[75],"quotient-converges":[77],"to":[78],"it.":[79],"In":[80],"addition,":[81],"explicitly":[83],"construct":[84],"such":[85],"increasing,":[88],"submodular,":[89],"and":[90,95],"upper":[91],"continuous":[92],"prove":[96],"completeness":[98],"space":[101],"under":[102],"quotient-convergence.":[103]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-01-29T00:00:00"}
