{"id":"https://openalex.org/W1522937572","doi":"https://doi.org/10.1007/3-540-45586-8_2","title":"Projection and Lifting in Combinatorial Optimization","display_name":"Projection and Lifting in Combinatorial Optimization","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1522937572","doi":"https://doi.org/10.1007/3-540-45586-8_2","mag":"1522937572"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45586-8_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45586-8_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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":["Mathematical Sciences Department, Carnegie Mellon University, Wean Hall, 15213, Pittsburgh, PA, USA"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Department, Carnegie Mellon University, Wean Hall, 15213, Pittsburgh, PA, 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":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.4324,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8989726,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"26","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9962999820709229,"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/T12288","display_name":"Optimization and Search Problems","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/polyhedron","display_name":"Polyhedron","score":0.8975192308425903},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6775342226028442},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5480287075042725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5274546146392822},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5255664587020874},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4825384020805359},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.475212424993515},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4659956693649292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42559194564819336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3068512976169586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2885732054710388},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11418244242668152}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8975192308425903},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6775342226028442},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5480287075042725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5274546146392822},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5255664587020874},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4825384020805359},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.475212424993515},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4659956693649292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42559194564819336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3068512976169586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2885732054710388},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11418244242668152}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-45586-8_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45586-8_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W36169824","https://openalex.org/W1487077091","https://openalex.org/W1494436834","https://openalex.org/W1522276212","https://openalex.org/W1529128749","https://openalex.org/W1545725275","https://openalex.org/W1578768378","https://openalex.org/W1869569149","https://openalex.org/W1965217041","https://openalex.org/W1968143987","https://openalex.org/W1970193303","https://openalex.org/W1972997295","https://openalex.org/W1975015343","https://openalex.org/W1985220893","https://openalex.org/W1985322505","https://openalex.org/W1997993610","https://openalex.org/W2003276565","https://openalex.org/W2005676331","https://openalex.org/W2010211888","https://openalex.org/W2021947147","https://openalex.org/W2023521867","https://openalex.org/W2032320685","https://openalex.org/W2035567981","https://openalex.org/W2039648193","https://openalex.org/W2041873708","https://openalex.org/W2046906980","https://openalex.org/W2049143039","https://openalex.org/W2049287714","https://openalex.org/W2049505431","https://openalex.org/W2058937865","https://openalex.org/W2064135070","https://openalex.org/W2065141624","https://openalex.org/W2065804773","https://openalex.org/W2080263450","https://openalex.org/W2093022060","https://openalex.org/W2106264302","https://openalex.org/W2151308681","https://openalex.org/W2152028777","https://openalex.org/W2399100674","https://openalex.org/W4210953350","https://openalex.org/W4236680666","https://openalex.org/W4253741566","https://openalex.org/W4285719527","https://openalex.org/W6651610120","https://openalex.org/W6681028219","https://openalex.org/W7029769179"],"related_works":["https://openalex.org/W2030718493","https://openalex.org/W2469464399","https://openalex.org/W2228244008","https://openalex.org/W2301583490","https://openalex.org/W2103429114","https://openalex.org/W2065436195","https://openalex.org/W4285278887","https://openalex.org/W2365237642","https://openalex.org/W2995925505","https://openalex.org/W3116484972"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}