{"id":"https://openalex.org/W2016428812","doi":"https://doi.org/10.1137/120899480","title":"Robust Independence Systems","display_name":"Robust Independence Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2016428812","doi":"https://doi.org/10.1137/120899480","mag":"2016428812"},"language":"en","primary_location":{"id":"doi:10.1137/120899480","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120899480","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047111221","display_name":"Naonori Kakimura","orcid":"https://orcid.org/0000-0002-3918-3479"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Naonori Kakimura","raw_affiliation_strings":["The University of Tokyo"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110768204","display_name":"Kazuhisa Makino","orcid":"https://orcid.org/0009-0000-9771-4955"},"institutions":[{"id":"https://openalex.org/I4210129581","display_name":"Kyoto University of Education","ror":"https://ror.org/03zhhr656","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210129581"]},{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhisa Makino","raw_affiliation_strings":["Kyoto univ"],"affiliations":[{"raw_affiliation_string":"Kyoto univ","institution_ids":["https://openalex.org/I22299242","https://openalex.org/I4210129581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047111221"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":0.7251,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71978458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"3","first_page":"1257","last_page":"1273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8800920248031616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7667621374130249},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.762991189956665},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6508097648620605},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.564653217792511},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.5430448055267334},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5225193500518799},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5225136280059814},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42379194498062134},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.14971426129341125}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8800920248031616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7667621374130249},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.762991189956665},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6508097648620605},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.564653217792511},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.5430448055267334},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5225193500518799},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5225136280059814},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42379194498062134},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.14971426129341125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120899480","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120899480","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1599161138","https://openalex.org/W1966923282","https://openalex.org/W1991528957","https://openalex.org/W2003476672","https://openalex.org/W2029846150","https://openalex.org/W2043260929","https://openalex.org/W2064594923","https://openalex.org/W2071350251","https://openalex.org/W2079266301","https://openalex.org/W2081254453","https://openalex.org/W2111741734","https://openalex.org/W2113437680","https://openalex.org/W2132651631","https://openalex.org/W2136442119","https://openalex.org/W2913331726","https://openalex.org/W3136714316"],"related_works":["https://openalex.org/W2058299944","https://openalex.org/W4233892543","https://openalex.org/W4323360720","https://openalex.org/W1550144461","https://openalex.org/W4252399622","https://openalex.org/W4320232260","https://openalex.org/W1499990180","https://openalex.org/W4241672388","https://openalex.org/W2088312182","https://openalex.org/W4287077747"],"abstract_inverted_index":{"An":[0],"independence":[1,34,98,162,201],"system":[2,99],"$\\mathcal{F}$":[3,79],"is":[4,37,56,80,87],"one":[5],"of":[6,16,41,45,69,110,123,173,181],"the":[7,31,42,70,84,108,121,158,182,204],"most":[8,89],"fundamental":[9],"combinatorial":[10],"concepts,":[11],"which":[12,36],"includes":[13,66],"a":[14,38,48,53,75,101,115],"variety":[15],"objects":[17],"in":[18,78,203],"graphs":[19],"and":[20,27,120,125,137,140,153,171,191],"hypergraphs":[21],"such":[22,164,188],"as":[23,165,189],"matchings,":[24,168],"stable":[25],"sets,":[26],"matroids.":[28,46],"We":[29,195],"discuss":[30],"robustness":[32,159,183],"for":[33,62,118,135,150,157,160,184],"systems,":[35],"natural":[39],"generalization":[40],"greedy":[43],"property":[44],"For":[47],"real":[49],"number":[50],"$\\alpha>":[51],"0$,":[52],"set":[54,76],"$X\\in\\mathcal{F}$":[55],"said":[57],"to":[58,200],"be":[59],"$\\alpha$-robust":[60],"if":[61,83],"any":[63],"$k$,":[64],"it":[65],"an":[67],"$\\alpha$-approximation":[68],"maximum":[71],"$k$-independent":[72,82],"set,":[73,104],"where":[74,105],"$Y$":[77],"called":[81],"size":[85],"$|Y|$":[86],"at":[88],"$k$.":[90],"In":[91],"this":[92],"paper,":[93],"we":[94,178],"show":[95],"that":[96],"every":[97],"has":[100],"$1/\\sqrt{\\mu(\\mathcal{F})}$-robust":[102],"independent":[103],"$\\mu(\\mathcal{F})$":[106],"denotes":[107],"exchangeability":[109],"$\\mathcal{F}$.":[111],"Our":[112],"result":[113,117],"contains":[114],"classical":[116],"matroids":[119],"ones":[122],"Hassin":[124],"Rubinstein":[126],"[SIAM":[127,142],"J.":[128,143],"Discrete":[129,144],"Math.,":[130,145],"15":[131],"(2002),":[132],"pp.":[133,148],"530--537]":[134],"matchings":[136],"Fujita,":[138],"Kobayashi,":[139],"Makino":[141],"27":[146],"(2013),":[147],"1234--1256]":[149],"matroid":[151,169],"$2$-intersections,":[152],"provides":[154],"better":[155],"bounds":[156,180],"many":[161],"systems":[163,202],"$b$-matchings,":[166],"hypergraph":[167],"$p$-intersections,":[170],"unions":[172],"vertex":[174],"disjoint":[175],"paths.":[176],"Furthermore,":[177],"provide":[179],"nonlinear":[185],"weight":[186,210],"functions":[187],"submodular":[190],"convex":[192],"quadratic":[193],"functions.":[194,211],"also":[196],"extend":[197],"our":[198],"results":[199],"integral":[205],"lattice":[206],"with":[207],"separable":[208],"concave":[209]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}