{"id":"https://openalex.org/W2124452917","doi":"https://doi.org/10.1007/bf01580440","title":"Facets of the knapsack polytope","display_name":"Facets of the knapsack polytope","publication_year":1975,"publication_date":"1975-12-01","ids":{"openalex":"https://openalex.org/W2124452917","doi":"https://doi.org/10.1007/bf01580440","mag":"2124452917"},"language":"en","primary_location":{"id":"doi:10.1007/bf01580440","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01580440","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5072070820","display_name":"Egon Balas","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Egon Balas","raw_affiliation_strings":["Carnegie-Mellon University, Pittsburgh, Pa., USA","Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072070820"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":27.0953,"has_fulltext":false,"cited_by_count":393,"citation_normalized_percentile":{"value":0.99498956,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"8","issue":"1","first_page":"146","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9368000030517578,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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":0.8732787370681763},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8413151502609253},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7649948596954346},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.7315553426742554},{"id":"https://openalex.org/keywords/facet","display_name":"Facet (psychology)","score":0.7290603518486023},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.7071893215179443},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6680648326873779},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5011212825775146},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.49915122985839844},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.4761359989643097},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.433888703584671},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.41054394841194153},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.2293064296245575},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.2073761522769928},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20463308691978455},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.19942492246627808},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.19807130098342896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12730330228805542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08572205901145935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8732787370681763},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8413151502609253},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7649948596954346},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.7315553426742554},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.7290603518486023},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.7071893215179443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6680648326873779},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5011212825775146},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.49915122985839844},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.4761359989643097},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.433888703584671},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.41054394841194153},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2293064296245575},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2073761522769928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20463308691978455},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.19942492246627808},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.19807130098342896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12730330228805542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08572205901145935},{"id":"https://openalex.org/C2865642","wikidata":"https://www.wikidata.org/wiki/Q378132","display_name":"Big Five personality traits","level":3,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C187288502","wikidata":"https://www.wikidata.org/wiki/Q641118","display_name":"Personality","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01580440","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01580440","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2006934540","https://openalex.org/W2049741107","https://openalex.org/W2075339720","https://openalex.org/W4235178139","https://openalex.org/W6604149353","https://openalex.org/W6678777597"],"related_works":["https://openalex.org/W2066333776","https://openalex.org/W4301600724","https://openalex.org/W4298021137","https://openalex.org/W2622142234","https://openalex.org/W2084236013","https://openalex.org/W29206020","https://openalex.org/W2510190638","https://openalex.org/W2090161266","https://openalex.org/W3105419662","https://openalex.org/W2064135070"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}