{"id":"https://openalex.org/W1976222519","doi":"https://doi.org/10.1002/net.3230240103","title":"Weighted <i>k</i>\u2010cardinality trees: Complexity and polyhedral structure","display_name":"Weighted <i>k</i>\u2010cardinality trees: Complexity and polyhedral structure","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W1976222519","doi":"https://doi.org/10.1002/net.3230240103","mag":"1976222519"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230240103","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230240103","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5019439480","display_name":"Matteo Fischetti","orcid":"https://orcid.org/0000-0001-6601-0568"},"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":false,"raw_author_name":"Matteo Fischetti","raw_affiliation_strings":["University of Padova, via Gradenigo 6/A, 35100 Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Padova, via Gradenigo 6/A, 35100 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111683448","display_name":"Horst W. Hamacher","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Horst W. Hamacher","raw_affiliation_strings":["Fach. Mathematik, University of Kaiserslautern, Postfach 30G9, D-6750 Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fach. Mathematik, University of Kaiserslautern, Postfach 30G9, D-6750 Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073826576","display_name":"Kurt J\u00f6rnsten","orcid":"https://orcid.org/0000-0001-9370-5285"},"institutions":[{"id":"https://openalex.org/I931913249","display_name":"Norwegian School of Economics","ror":"https://ror.org/04v53s997","country_code":"NO","type":"education","lineage":["https://openalex.org/I931913249"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Kurt J\u00f8rnsten","raw_affiliation_strings":["Dept. of Finance and M. Sci, Norwegian School of Bus. Adm., Helleveien 30, N-5035 Bergen, Norway","Dept. of Finance and M. Sci, Norwegian School of Bus. Adm., Helleveien 30, N\u20105035 Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Finance and M. Sci, Norwegian School of Bus. Adm., Helleveien 30, N-5035 Bergen, Norway","institution_ids":["https://openalex.org/I931913249"]},{"raw_affiliation_string":"Dept. of Finance and M. Sci, Norwegian School of Bus. Adm., Helleveien 30, N\u20105035 Bergen, Norway","institution_ids":["https://openalex.org/I931913249"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053677027","display_name":"Francesco Maffioli","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Maffioli","raw_affiliation_strings":["Politecnico di Milano, Dip. di Elettronica e Informazione, piazza L. da Vinci 32, 20133 Milano, Italy","Politecnico di Milano, Dip. di Elettronica e Informazione, Piazza L. da Vinci 32, 20133 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico di Milano, Dip. di Elettronica e Informazione, piazza L. da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Politecnico di Milano, Dip. di Elettronica e Informazione, Piazza L. da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":5.3863,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.97106205,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"11","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11630","display_name":"Petroleum Processing and Analysis","score":0.9603000283241272,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11630","display_name":"Petroleum Processing and Analysis","score":0.9603000283241272,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11053","display_name":"Process Optimization and Integration","score":0.9200999736785889,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T12072","display_name":"Machine Learning and Algorithms","score":0.9097999930381775,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.7415605187416077},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7257794141769409},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.640913724899292},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5800528526306152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5469269752502441},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5307405591011047},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.49360764026641846},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.489362895488739},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46855148673057556},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44979381561279297},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.437979131937027},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4150826930999756},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41430097818374634},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.411009281873703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3315061926841736},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28314027190208435}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7415605187416077},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7257794141769409},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.640913724899292},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5800528526306152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5469269752502441},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5307405591011047},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.49360764026641846},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.489362895488739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46855148673057556},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44979381561279297},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.437979131937027},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4150826930999756},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41430097818374634},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.411009281873703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3315061926841736},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28314027190208435},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230240103","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230240103","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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":6,"referenced_works":["https://openalex.org/W2011039300","https://openalex.org/W2017927472","https://openalex.org/W2023721044","https://openalex.org/W2031869856","https://openalex.org/W2060953011","https://openalex.org/W2075030161"],"related_works":["https://openalex.org/W2916043681","https://openalex.org/W2896131632","https://openalex.org/W4280529077","https://openalex.org/W2391438543","https://openalex.org/W2997473813","https://openalex.org/W2008231869","https://openalex.org/W323119424","https://openalex.org/W2030718493","https://openalex.org/W2469464399","https://openalex.org/W2103429114"],"abstract_inverted_index":{"Abstract":[0],"We":[1,62],"consider":[2],"the":[3,9,39,90,94],"k":[4,22,69],"\u2010CARD":[5,70],"TREE":[6,71],"problem,":[7],"i.e.,":[8],"problem":[10,30,41],"of":[11,28,68,81,89,93],"finding":[12],"in":[13,32,53],"a":[14,19,60,79],"given":[15],"undirected":[16],"graph":[17],"G":[18,57],"subtree":[20],"with":[21],"edges,":[23],"having":[24],"minimum":[25],"weight.":[26],"Applications":[27],"this":[29],"arise":[31],"oil\u2010field":[33],"leasing":[34],"and":[35,72],"facility":[36],"layout.":[37],"Although":[38],"general":[40],"is":[42,58,97],"shown":[43],"to":[44],"be":[45,51],"strongly":[46],"NP":[47],"hard,":[48],"it":[49],"can":[50],"solved":[52],"polynomial":[54],"time":[55],"if":[56],"itself":[59],"tree.":[61],"give":[63],"an":[64,73],"integer":[65,95],"programming":[66],"formulation":[67],"efficient":[74],"exact":[75],"separation":[76],"routine":[77],"for":[78],"set":[80],"generalized":[82],"subtour":[83],"elimination":[84],"constraints.":[85],"The":[86],"polyhedral":[87],"structure":[88],"convex":[91],"hull":[92],"solutions":[96],"studied.":[98],"\u00a9":[99],"1994":[100],"by":[101],"John":[102],"Wiley":[103],"&amp;":[104],"Sons,":[105],"Inc.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}