{"id":"https://openalex.org/W2077333323","doi":"https://doi.org/10.1137/0401031","title":"A Class of Polynomially Solvable Set-Covering Problems","display_name":"A Class of Polynomially Solvable Set-Covering Problems","publication_year":1988,"publication_date":"1988-08-01","ids":{"openalex":"https://openalex.org/W2077333323","doi":"https://doi.org/10.1137/0401031","mag":"2077333323"},"language":"en","primary_location":{"id":"doi:10.1137/0401031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0401031","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/A5074793077","display_name":"Paola Bertolazzi","orcid":"https://orcid.org/0000-0002-2249-1993"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Bertolazzi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000113494","display_name":"Antonio Sassano","orcid":"https://orcid.org/0000-0002-1458-2449"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Sassano","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1431,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.87450563,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":"3","first_page":"306","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.96670001745224,"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":0.96670001745224,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9521999955177307,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.934499979019165,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.9075711965560913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.817782461643219},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8137503266334534},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7551934719085693},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.721315860748291},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.711249589920044},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6208162903785706},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5966119766235352},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5178304314613342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.513088583946228},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.4623149335384369},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.42192184925079346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08185717463493347}],"concepts":[{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.9075711965560913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.817782461643219},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8137503266334534},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7551934719085693},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.721315860748291},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.711249589920044},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6208162903785706},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5966119766235352},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5178304314613342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.513088583946228},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.4623149335384369},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.42192184925079346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08185717463493347},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0401031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0401031","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"},{"id":"pmh:hdl:10068/317912","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/317912","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Y - Progress report"},{"id":"pmh:oai:iris.uniroma1.it:11573/427904","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/427904","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1799057383","https://openalex.org/W1969423858","https://openalex.org/W1981295749","https://openalex.org/W2051364416"],"related_works":["https://openalex.org/W1647473158","https://openalex.org/W2951921012","https://openalex.org/W4299819511","https://openalex.org/W2063583565","https://openalex.org/W2380771436","https://openalex.org/W2006784845","https://openalex.org/W2374487760","https://openalex.org/W4251106365","https://openalex.org/W2087066","https://openalex.org/W2057256624"],"abstract_inverted_index":{"A":[0,41],"clutterL":[1],"is":[2,34,45,76,110,126],"a":[3,9,46,73,106,129],"collection":[4],"of":[5,8,43,48,62,66,72,88,96,100,105,122,137],"m":[6,132],"subsets":[7],"ground":[10],"set":[11],"$E(":[12,49],"L":[13,44,50,75,115],")":[14],"=":[15],"\\{":[16],"x_1":[17],",":[18],"\\cdots":[19],",x_n":[20],"\\}$":[21],"with":[22,59],"the":[23,68,79,86,94,98,103,117,120],"property":[24,118],"that":[25,91,119],"for":[26,146],"every":[27],"pair":[28],"$A_i":[29],",A_j":[30],"\\in":[31],"L,A_i":[32],"$":[33],"neither":[35],"contained":[36],"nor":[37],"contains":[38,93],"$A_j":[39],"$.":[40],"transversal":[42,71,154],"subset":[47],")$":[51],"having":[52],"at":[53],"least":[54],"one":[55],"element":[56],"in":[57,131],"common":[58],"each":[60],"member":[61],"L.":[63],"The":[64,135],"problem":[65],"finding":[67,150],"minimum":[69,152],"weight":[70,153],"clutter":[74,114],"equivalent":[77],"to":[78],"well-known":[80],"set-covering":[81],"problem.":[82],"In":[83],"this":[84],"paper":[85],"class":[87,95],"ideal":[89,113,138],"clutters":[90,97,139],"properly":[92],"members":[99],"which":[101],"are":[102,140,155],"bases":[104],"matroid":[107],"(matroidal":[108],"clutters)":[109],"introduced.":[111],"An":[112],"has":[116],"number":[121],"its":[123],"minimal":[124],"transversals":[125],"bounded":[127],"by":[128],"polynomial":[130,144],"and":[133,142,149],"n.":[134],"properties":[136],"described,":[141],"two":[143],"algorithms":[145],"recognizing":[147],"them":[148],"their":[151],"presented.":[156]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}