{"id":"https://openalex.org/W2956015669","doi":"https://doi.org/10.1137/0206041","title":"An Analysis of Several Heuristics for the Traveling Salesman Problem","display_name":"An Analysis of Several Heuristics for the Traveling Salesman Problem","publication_year":1977,"publication_date":"1977-09-01","ids":{"openalex":"https://openalex.org/W2956015669","doi":"https://doi.org/10.1137/0206041","mag":"2956015669"},"language":"en","primary_location":{"id":"doi:10.1137/0206041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0206041","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5009388396","display_name":"Daniel J. Rosenkrantz","orcid":"https://orcid.org/0000-0002-7044-0197"},"institutions":[{"id":"https://openalex.org/I4210092162","display_name":"General Electric (Israel)","ror":"https://ror.org/00fymn751","country_code":"IL","type":"company","lineage":["https://openalex.org/I1332737386","https://openalex.org/I4210092162"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Daniel J. Rosenkrantz","raw_affiliation_strings":["General Electric Research and Development Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Electric Research and Development Center","institution_ids":["https://openalex.org/I4210092162"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052202085","display_name":"Richard E. Stearns","orcid":"https://orcid.org/0000-0001-5058-1999"},"institutions":[{"id":"https://openalex.org/I4210092162","display_name":"General Electric (Israel)","ror":"https://ror.org/00fymn751","country_code":"IL","type":"company","lineage":["https://openalex.org/I1332737386","https://openalex.org/I4210092162"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Richard E. Stearns","raw_affiliation_strings":["General Electric Research and Development Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Electric Research and Development Center","institution_ids":["https://openalex.org/I4210092162"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109259127","display_name":"Philip Lewis","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092162","display_name":"General Electric (Israel)","ror":"https://ror.org/00fymn751","country_code":"IL","type":"company","lineage":["https://openalex.org/I1332737386","https://openalex.org/I4210092162"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Philip M. Lewis, II","raw_affiliation_strings":["General Electric Research and Development Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Electric Research and Development Center","institution_ids":["https://openalex.org/I4210092162"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009388396"],"corresponding_institution_ids":["https://openalex.org/I4210092162"],"apc_list":null,"apc_paid":null,"fwci":10.1234,"has_fulltext":false,"cited_by_count":798,"citation_normalized_percentile":{"value":0.97856615,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":"3","first_page":"563","last_page":"581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9979000091552734,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9944999814033508,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.8432960510253906},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7679166793823242},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7211567163467407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7181886434555054},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7022220492362976},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5966536998748779},{"id":"https://openalex.org/keywords/christofides-algorithm","display_name":"Christofides algorithm","score":0.5201242566108704},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5145778059959412},{"id":"https://openalex.org/keywords/competitive-analysis","display_name":"Competitive analysis","score":0.47673356533050537},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.4509250819683075},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.4371374845504761},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.42712461948394775},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.398784339427948},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25960177183151245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20919060707092285}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8432960510253906},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7679166793823242},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7211567163467407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7181886434555054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7022220492362976},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5966536998748779},{"id":"https://openalex.org/C138600008","wikidata":"https://www.wikidata.org/wiki/Q498144","display_name":"Christofides algorithm","level":4,"score":0.5201242566108704},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5145778059959412},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.47673356533050537},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.4509250819683075},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.4371374845504761},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.42712461948394775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.398784339427948},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25960177183151245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20919060707092285},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0206041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0206041","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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":14,"referenced_works":["https://openalex.org/W1965680834","https://openalex.org/W1968766664","https://openalex.org/W1991529799","https://openalex.org/W2007572995","https://openalex.org/W2017927472","https://openalex.org/W2042986967","https://openalex.org/W2056898464","https://openalex.org/W2106378689","https://openalex.org/W2119606130","https://openalex.org/W2148673189","https://openalex.org/W2167890858","https://openalex.org/W2401610261","https://openalex.org/W3118260104","https://openalex.org/W4252166328"],"related_works":["https://openalex.org/W4200179302","https://openalex.org/W1595757466","https://openalex.org/W4389782626","https://openalex.org/W2766731260","https://openalex.org/W3210931532","https://openalex.org/W2620231896","https://openalex.org/W1645834615","https://openalex.org/W87675801","https://openalex.org/W2171568915","https://openalex.org/W2055574289"],"abstract_inverted_index":{"Several":[0],"polynomial":[1],"time":[2],"algorithms":[3],"finding":[4],"\u201cgood,\u201d":[5],"but":[6,157],"not":[7],"necessarily":[8],"optimal,":[9],"tours":[10,147],"for":[11,134,158],"the":[12,20,26,29,34,39,45,55,67,105,160],"traveling":[13,140],"salesman":[14,141],"problem":[15],"are":[16,79,83,119,139],"considered.":[17],"We":[18,59],"measure":[19],"closeness":[21],"of":[22,28,54,57,72,115],"a":[23,51,62,88,111],"tour":[24,31,36],"by":[25,50,152],"ratio":[27,46,106,161],"obtained":[30],"length":[32],"to":[33,86,109,125],"minimal":[35],"length.":[37],"For":[38,92],"nearest":[40,100],"neighbor":[41],"method,":[42],"we":[43,75,98],"show":[44],"is":[47,107,130,162],"bounded":[48],"above":[49],"logarithmic":[52,63,89],"function":[53],"number":[56],"nodes.":[58],"also":[60,84,131],"provide":[61],"lower":[64],"bound":[65,114],"on":[66],"worst":[68],"case.":[69],"A":[70],"class":[71],"approximation":[73],"methods":[74,78],"call":[76,99],"insertion":[77,95,101],"studied,":[80],"and":[81,102,117],"these":[82],"shown":[85,108,132],"have":[87,110],"upper":[90,113,127],"bound.":[91,128],"two":[93],"specific":[94],"methods,":[96],"which":[97,148,159],"cheapest":[103],"insertion,":[104],"constant":[112],"2,":[116],"examples":[118],"provided":[120],"that":[121,133],"come":[122],"arbitrarily":[123],"close":[124],"this":[126],"It":[129],"any":[135],"$n\\geqq":[136],"8$,":[137],"there":[138],"problems":[142],"with":[143],"n":[144],"nodes":[145],"having":[146],"cannot":[149],"be":[150],"improved":[151],"making":[153],"$n/4$":[154],"edge":[155],"changes,":[156],"$2(1-1/n)$.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":40},{"year":2024,"cited_by_count":47},{"year":2023,"cited_by_count":40},{"year":2022,"cited_by_count":33},{"year":2021,"cited_by_count":44},{"year":2020,"cited_by_count":35},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":29},{"year":2017,"cited_by_count":30},{"year":2016,"cited_by_count":25},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":32},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":23}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}