{"id":"https://openalex.org/W2135149549","doi":"https://doi.org/10.1137/s0036144596297514","title":"Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey","display_name":"Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2135149549","doi":"https://doi.org/10.1137/s0036144596297514","mag":"2135149549"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144596297514","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144596297514","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.tue.nl/en/publications/bf5023cd-7df0-43f4-884d-1de905a9395b","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044307799","display_name":"Rainer E. Burkard","orcid":null},"institutions":[{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rainer E. Burkard","raw_affiliation_strings":["Institute of Discrete Mathematics (5050)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics (5050)","institution_ids":["https://openalex.org/I2799411422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013475667","display_name":"Vladimir G. De\u0131\u030cneko","orcid":"https://orcid.org/0000-0002-0079-4299"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Vladimir G. Deineko","raw_affiliation_strings":[", Graz University of Technology#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", Graz University of Technology#TAB#","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058005331","display_name":"Ren\u00e9 van Dal","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 van Dal","raw_affiliation_strings":["Chalmers Tekniska H\u00f6gskola, Institutionen f\u00f6r Datavetenskap, S-41296 G\u00f6teborg, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chalmers Tekniska H\u00f6gskola, Institutionen f\u00f6r Datavetenskap, S-41296 G\u00f6teborg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001418639","display_name":"Jack A.A. van der Veen","orcid":"https://orcid.org/0000-0003-4756-3831"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jack A. A. van der Veen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080746477","display_name":"Gerhard J. Woeginger","orcid":"https://orcid.org/0000-0001-8816-2693"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerhard J. Woeginger","raw_affiliation_strings":["Stochastics W&I"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stochastics W&I","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5044307799"],"corresponding_institution_ids":["https://openalex.org/I2799411422"],"apc_list":null,"apc_paid":null,"fwci":11.2454,"has_fulltext":true,"cited_by_count":166,"citation_normalized_percentile":{"value":0.98666355,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"496","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9975000023841858,"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":0.9975000023841858,"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/T11106","display_name":"Data Management and Algorithms","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9912999868392944,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.9674172401428223},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.6753638982772827},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.5365671515464783},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5102648735046387},{"id":"https://openalex.org/keywords/lin\u2013kernighan-heuristic","display_name":"Lin\u2013Kernighan heuristic","score":0.4916570782661438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49126189947128296},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.4697924852371216},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4403277635574341},{"id":"https://openalex.org/keywords/cross-entropy-method","display_name":"Cross-entropy method","score":0.4147280156612396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4105822443962097},{"id":"https://openalex.org/keywords/quadratic-assignment-problem","display_name":"Quadratic assignment problem","score":0.38056784868240356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3458777666091919}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.9674172401428223},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.6753638982772827},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.5365671515464783},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5102648735046387},{"id":"https://openalex.org/C103888782","wikidata":"https://www.wikidata.org/wiki/Q2835802","display_name":"Lin\u2013Kernighan heuristic","level":4,"score":0.4916570782661438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49126189947128296},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.4697924852371216},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4403277635574341},{"id":"https://openalex.org/C75782508","wikidata":"https://www.wikidata.org/wiki/Q3333633","display_name":"Cross-entropy method","level":4,"score":0.4147280156612396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4105822443962097},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.38056784868240356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3458777666091919}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036144596297514","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144596297514","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/bf5023cd-7df0-43f4-884d-1de905a9395b","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/bf5023cd-7df0-43f4-884d-1de905a9395b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Burkard, R E, Deineko, V G, Dal, van, R, Veen, van der, J A A & Woeginger, G J 1998, 'Well-solvable special cases of the Traveling Salesman Problem : a survey', SIAM Review, vol. 40, no. 3, pp. 496-546. https://doi.org/10.1137/S0036144596297514","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:680109","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=680109","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0036-1445","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:680109","is_oa":false,"landing_page_url":"http://repository.tue.nl/680109","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0036-1445","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/bf5023cd-7df0-43f4-884d-1de905a9395b","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/bf5023cd-7df0-43f4-884d-1de905a9395b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Review, 40(3), 496 - 546. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/bf5023cd-7df0-43f4-884d-1de905a9395b","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/bf5023cd-7df0-43f4-884d-1de905a9395b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Burkard, R E, Deineko, V G, Dal, van, R, Veen, van der, J A A & Woeginger, G J 1998, 'Well-solvable special cases of the Traveling Salesman Problem : a survey', SIAM Review, vol. 40, no. 3, pp. 496-546. https://doi.org/10.1137/S0036144596297514","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.44999998807907104,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":94,"referenced_works":["https://openalex.org/W789583781","https://openalex.org/W1484914719","https://openalex.org/W1486813196","https://openalex.org/W1491169489","https://openalex.org/W1583471982","https://openalex.org/W1964127155","https://openalex.org/W1964794163","https://openalex.org/W1968919074","https://openalex.org/W1970388956","https://openalex.org/W1971327934","https://openalex.org/W1972819258","https://openalex.org/W1976225909","https://openalex.org/W1977852789","https://openalex.org/W1981894795","https://openalex.org/W1986033901","https://openalex.org/W1991737330","https://openalex.org/W1994863634","https://openalex.org/W1996800651","https://openalex.org/W1999466794","https://openalex.org/W2001248734","https://openalex.org/W2003687734","https://openalex.org/W2005314985","https://openalex.org/W2009175527","https://openalex.org/W2011919427","https://openalex.org/W2011993797","https://openalex.org/W2012759844","https://openalex.org/W2016168023","https://openalex.org/W2017932090","https://openalex.org/W2020813360","https://openalex.org/W2021199373","https://openalex.org/W2027236728","https://openalex.org/W2029841189","https://openalex.org/W2034489885","https://openalex.org/W2035704018","https://openalex.org/W2038774649","https://openalex.org/W2038906000","https://openalex.org/W2040031786","https://openalex.org/W2040271493","https://openalex.org/W2041758482","https://openalex.org/W2042706779","https://openalex.org/W2042986967","https://openalex.org/W2043589600","https://openalex.org/W2043641066","https://openalex.org/W2044060832","https://openalex.org/W2049591070","https://openalex.org/W2050718739","https://openalex.org/W2054977621","https://openalex.org/W2055257826","https://openalex.org/W2055336889","https://openalex.org/W2055569927","https://openalex.org/W2063528310","https://openalex.org/W2066906739","https://openalex.org/W2076341540","https://openalex.org/W2077843935","https://openalex.org/W2078993594","https://openalex.org/W2079698947","https://openalex.org/W2080333071","https://openalex.org/W2082378428","https://openalex.org/W2083210138","https://openalex.org/W2086091870","https://openalex.org/W2086315201","https://openalex.org/W2087058588","https://openalex.org/W2089099831","https://openalex.org/W2089810121","https://openalex.org/W2089929819","https://openalex.org/W2090365531","https://openalex.org/W2092501917","https://openalex.org/W2092845562","https://openalex.org/W2100931500","https://openalex.org/W2101116363","https://openalex.org/W2105016507","https://openalex.org/W2115702407","https://openalex.org/W2116418681","https://openalex.org/W2119735681","https://openalex.org/W2125292347","https://openalex.org/W2139648082","https://openalex.org/W2145466017","https://openalex.org/W2151811408","https://openalex.org/W2170954130","https://openalex.org/W2317566604","https://openalex.org/W2323986888","https://openalex.org/W2324108981","https://openalex.org/W2325186291","https://openalex.org/W2333874445","https://openalex.org/W2413690630","https://openalex.org/W2501346809","https://openalex.org/W2743045177","https://openalex.org/W3000633136","https://openalex.org/W4231672148","https://openalex.org/W4236296313","https://openalex.org/W4238913003","https://openalex.org/W4243078096","https://openalex.org/W4244086314","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1595757466","https://openalex.org/W2189435634","https://openalex.org/W2592065458","https://openalex.org/W1563568831","https://openalex.org/W4210470436","https://openalex.org/W588755621","https://openalex.org/W4200602616","https://openalex.org/W4224271060","https://openalex.org/W2572756133","https://openalex.org/W2135149549"],"abstract_inverted_index":{"The":[0],"traveling":[1],"salesman":[2],"problem":[3],"(TSP)":[4],"belongs":[5],"to":[6],"the":[7,46,53],"most":[8,10,13],"basic,":[9],"important,":[11],"and":[12,68],"investigated":[14],"problems":[15],"in":[16,35],"combinatorial":[17],"optimization.":[18],"Although":[19],"it":[20],"is":[21],"an":[22,59],"${\\cal":[23],"NP}$-hard":[24],"problem,":[25],"many":[26],"of":[27,76],"its":[28],"special":[29,41],"cases":[30,42],"can":[31],"be":[32],"solved":[33],"efficiently":[34],"polynomial":[36],"time.":[37],"We":[38],"survey":[39,57,61],"these":[40],"with":[43],"emphasis":[44],"on":[45],"results":[47],"that":[48],"have":[49],"been":[50],"obtained":[51],"during":[52],"decade":[54],"1985--1995.":[55],"This":[56],"complements":[58],"earlier":[60],"from":[62],"1985":[63],"compiled":[64],"by":[65],"Gilmore,":[66],"Lawler,":[67],"Shmoys":[69],"[The":[70],"Traveling":[71],"Salesman":[72],"Problem---A":[73],"Guided":[74],"Tour":[75],"Combinatorial":[77],"Optimization,":[78],"Wiley,":[79],"Chichester,":[80],"pp.":[81],"87--143].":[82]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":10}],"updated_date":"2026-05-18T08:16:58.900851","created_date":"2025-10-10T00:00:00"}