{"id":"https://openalex.org/W2021659530","doi":"https://doi.org/10.1007/bf01585563","title":"Worst-case comparison of valid inequalities for the TSP","display_name":"Worst-case comparison of valid inequalities for the TSP","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2021659530","doi":"https://doi.org/10.1007/bf01585563","mag":"2021659530"},"language":"en","primary_location":{"id":"doi:10.1007/bf01585563","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585563","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/A5112864313","display_name":"Michel X. Goemans","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michel X. Goemans","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Room 2-382, 02139-4307, Cambridge, MA, USA","Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Room 2-382, 02139-4307, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112864313"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":14.8677,"has_fulltext":false,"cited_by_count":146,"citation_normalized_percentile":{"value":0.99119464,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"69","issue":"1-3","first_page":"335","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9934999942779541,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9934999942779541,"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/T12176","display_name":"Optimization and Packing Problems","score":0.991599977016449,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.974399983882904,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.804230809211731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7263251543045044},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.6698656678199768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6347973942756653},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5484510064125061},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5249823927879333},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5069479942321777},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5024600028991699},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4140346646308899},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4124062955379486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35780853033065796},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24949654936790466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20857632160186768},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08105546236038208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07497644424438477}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.804230809211731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7263251543045044},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.6698656678199768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6347973942756653},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5484510064125061},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5249823927879333},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5069479942321777},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5024600028991699},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4140346646308899},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4124062955379486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35780853033065796},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24949654936790466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20857632160186768},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08105546236038208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07497644424438477},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bf01585563","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585563","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.1702","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.1702","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-math.mit.edu/~goemans/PAPERS/Goemans-1995-WorstCaseComparisonOfValidInequalitiesForTheTSP.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.8008","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.8008","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://theory.lcs.mit.edu/pub/people/goemans/tsp.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W5720473","https://openalex.org/W30880036","https://openalex.org/W83064900","https://openalex.org/W954848844","https://openalex.org/W1482143660","https://openalex.org/W1714357736","https://openalex.org/W1964127155","https://openalex.org/W1981894795","https://openalex.org/W1991119408","https://openalex.org/W2009803313","https://openalex.org/W2012759844","https://openalex.org/W2020163691","https://openalex.org/W2021199373","https://openalex.org/W2027868217","https://openalex.org/W2029242918","https://openalex.org/W2033662447","https://openalex.org/W2049591070","https://openalex.org/W2063836932","https://openalex.org/W2066580436","https://openalex.org/W2067684024","https://openalex.org/W2072789827","https://openalex.org/W2081290549","https://openalex.org/W2083210138","https://openalex.org/W2084340826","https://openalex.org/W2086315201","https://openalex.org/W2087508734","https://openalex.org/W2114552889","https://openalex.org/W2134092250","https://openalex.org/W2161305900","https://openalex.org/W2260470032","https://openalex.org/W2324108981","https://openalex.org/W2912533262"],"related_works":["https://openalex.org/W2916043681","https://openalex.org/W2896131632","https://openalex.org/W2391438543","https://openalex.org/W2997473813","https://openalex.org/W2008231869","https://openalex.org/W323119424","https://openalex.org/W2551069560","https://openalex.org/W2522231841","https://openalex.org/W2327310844","https://openalex.org/W4250631474"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}