{"id":"https://openalex.org/W4411887316","doi":"https://doi.org/10.1007/s10479-025-06641-5","title":"A survey on approximability of traveling salesman problems using the TSP-T3CO definition scheme","display_name":"A survey on approximability of traveling salesman problems using the TSP-T3CO definition scheme","publication_year":2025,"publication_date":"2025-07-01","ids":{"openalex":"https://openalex.org/W4411887316","doi":"https://doi.org/10.1007/s10479-025-06641-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-025-06641-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-025-06641-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-025-06641-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-025-06641-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091395244","display_name":"Sophia Saller","orcid":"https://orcid.org/0000-0003-4817-8601"},"institutions":[{"id":"https://openalex.org/I2802442800","display_name":"Deutsches Forschungsnetz","ror":"https://ror.org/038t94116","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2802442800"]},{"id":"https://openalex.org/I33256026","display_name":"German Research Centre for Artificial Intelligence","ror":"https://ror.org/01ayc5b57","country_code":"DE","type":"funder","lineage":["https://openalex.org/I33256026"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sophia Saller","raw_affiliation_strings":["Deutsches Forschungszentrum f\u00fcr K\u00fcnstliche Intelligenz, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Deutsches Forschungszentrum f\u00fcr K\u00fcnstliche Intelligenz, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I2802442800","https://openalex.org/I33256026"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017053713","display_name":"Jana Koehler","orcid":"https://orcid.org/0000-0001-9000-9188"},"institutions":[{"id":"https://openalex.org/I81007117","display_name":"Lucerne University of Applied Sciences and Arts","ror":"https://ror.org/04nd0xd48","country_code":"CH","type":"education","lineage":["https://openalex.org/I81007117"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Jana Koehler","raw_affiliation_strings":["Lucerne University of Applied Sciences and Arts, Lucerne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Lucerne University of Applied Sciences and Arts, Lucerne, Switzerland","institution_ids":["https://openalex.org/I81007117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015328592","display_name":"Andreas Karrenbauer","orcid":"https://orcid.org/0000-0001-6129-3220"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Karrenbauer","raw_affiliation_strings":["Max Planck Institute for Informatics, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Informatics, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091395244"],"corresponding_institution_ids":["https://openalex.org/I2802442800","https://openalex.org/I33256026"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22456673,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"351","issue":"3","first_page":"2129","last_page":"2190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9995999932289124,"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":0.9995999932289124,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9976000189781189,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8979910016059875},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.8614041805267334},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.7551324963569641},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.569258987903595},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5314908027648926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4507567286491394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44284215569496155},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.42560875415802},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21025201678276062}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8979910016059875},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.8614041805267334},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.7551324963569641},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.569258987903595},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5314908027648926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4507567286491394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44284215569496155},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.42560875415802},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21025201678276062},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10479-025-06641-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-025-06641-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-025-06641-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/330620","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/330620","pdf_url":"https://www.econstor.eu/bitstream/10419/330620/1/10479_2025_Article_6641.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10479-025-06641-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-025-06641-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-025-06641-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411887316.pdf","grobid_xml":"https://content.openalex.org/works/W4411887316.grobid-xml"},"referenced_works_count":214,"referenced_works":["https://openalex.org/W36531276","https://openalex.org/W151090950","https://openalex.org/W156319294","https://openalex.org/W174230839","https://openalex.org/W634463279","https://openalex.org/W882058369","https://openalex.org/W964861289","https://openalex.org/W1208385249","https://openalex.org/W1481773530","https://openalex.org/W1482405521","https://openalex.org/W1488422606","https://openalex.org/W1517470327","https://openalex.org/W1537819703","https://openalex.org/W1544163123","https://openalex.org/W1546311336","https://openalex.org/W1550422722","https://openalex.org/W1555563750","https://openalex.org/W1557293446","https://openalex.org/W1563055883","https://openalex.org/W1569858782","https://openalex.org/W1571087346","https://openalex.org/W1601649239","https://openalex.org/W1755312702","https://openalex.org/W1862548325","https://openalex.org/W1966209162","https://openalex.org/W1966981470","https://openalex.org/W1967197960","https://openalex.org/W1968429519","https://openalex.org/W1968594877","https://openalex.org/W1972398006","https://openalex.org/W1977129671","https://openalex.org/W1978101274","https://openalex.org/W1981245140","https://openalex.org/W1982028039","https://openalex.org/W1983002996","https://openalex.org/W1985142991","https://openalex.org/W1986056047","https://openalex.org/W1988227855","https://openalex.org/W1990313671","https://openalex.org/W1991149726","https://openalex.org/W1992249619","https://openalex.org/W1992447230","https://openalex.org/W1993433489","https://openalex.org/W1994184140","https://openalex.org/W1994248285","https://openalex.org/W1995284651","https://openalex.org/W1996011776","https://openalex.org/W1997715032","https://openalex.org/W1998678640","https://openalex.org/W1999401924","https://openalex.org/W1999799345","https://openalex.org/W2001139415","https://openalex.org/W2001994662","https://openalex.org/W2003281104","https://openalex.org/W2004512957","https://openalex.org/W2004604480","https://openalex.org/W2008656089","https://openalex.org/W2011230269","https://openalex.org/W2013525683","https://openalex.org/W2014979043","https://openalex.org/W2018269848","https://openalex.org/W2021012767","https://openalex.org/W2022563199","https://openalex.org/W2022980325","https://openalex.org/W2031236641","https://openalex.org/W2033660702","https://openalex.org/W2037666581","https://openalex.org/W2038190710","https://openalex.org/W2039097929","https://openalex.org/W2039766013","https://openalex.org/W2040678783","https://openalex.org/W2042251310","https://openalex.org/W2044119054","https://openalex.org/W2045526507","https://openalex.org/W2047386472","https://openalex.org/W2049287714","https://openalex.org/W2054669984","https://openalex.org/W2055406384","https://openalex.org/W2057559819","https://openalex.org/W2057741299","https://openalex.org/W2059222268","https://openalex.org/W2059615070","https://openalex.org/W2060827745","https://openalex.org/W2061637847","https://openalex.org/W2063277077","https://openalex.org/W2063961786","https://openalex.org/W2064816527","https://openalex.org/W2064935422","https://openalex.org/W2065166038","https://openalex.org/W2065889460","https://openalex.org/W2068752469","https://openalex.org/W2072136110","https://openalex.org/W2072400378","https://openalex.org/W2072484718","https://openalex.org/W2072592433","https://openalex.org/W2077694070","https://openalex.org/W2079487902","https://openalex.org/W2082353536","https://openalex.org/W2090486865","https://openalex.org/W2091368663","https://openalex.org/W2091637374","https://openalex.org/W2092293193","https://openalex.org/W2095032305","https://openalex.org/W2096305430","https://openalex.org/W2102862828","https://openalex.org/W2106727356","https://openalex.org/W2110367141","https://openalex.org/W2111563176","https://openalex.org/W2112686410","https://openalex.org/W2113873983","https://openalex.org/W2113939799","https://openalex.org/W2115273337","https://openalex.org/W2119709400","https://openalex.org/W2120988215","https://openalex.org/W2123087902","https://openalex.org/W2135149549","https://openalex.org/W2136400551","https://openalex.org/W2137717103","https://openalex.org/W2140787410","https://openalex.org/W2141481566","https://openalex.org/W2145145566","https://openalex.org/W2150483730","https://openalex.org/W2151239055","https://openalex.org/W2155735286","https://openalex.org/W2158175311","https://openalex.org/W2158591664","https://openalex.org/W2158999695","https://openalex.org/W2162344698","https://openalex.org/W2163428398","https://openalex.org/W2163873159","https://openalex.org/W2165758382","https://openalex.org/W2168155808","https://openalex.org/W2170739645","https://openalex.org/W2174834537","https://openalex.org/W2233419640","https://openalex.org/W2240814884","https://openalex.org/W2262276395","https://openalex.org/W2278286793","https://openalex.org/W2395335465","https://openalex.org/W2399100674","https://openalex.org/W2401610261","https://openalex.org/W2522091059","https://openalex.org/W2559541197","https://openalex.org/W2564703335","https://openalex.org/W2566339654","https://openalex.org/W2581478119","https://openalex.org/W2610052675","https://openalex.org/W2614086467","https://openalex.org/W2617045890","https://openalex.org/W2617377437","https://openalex.org/W2622090745","https://openalex.org/W2734875663","https://openalex.org/W2739408905","https://openalex.org/W2800453060","https://openalex.org/W2885246356","https://openalex.org/W2899200421","https://openalex.org/W2909651232","https://openalex.org/W2932662651","https://openalex.org/W2942047857","https://openalex.org/W2949660560","https://openalex.org/W2951508903","https://openalex.org/W2962875727","https://openalex.org/W2963750353","https://openalex.org/W2988480584","https://openalex.org/W2994010944","https://openalex.org/W2994566040","https://openalex.org/W3003532379","https://openalex.org/W3021677663","https://openalex.org/W3023471578","https://openalex.org/W3035464720","https://openalex.org/W3035754533","https://openalex.org/W3036941816","https://openalex.org/W3044025645","https://openalex.org/W3096239448","https://openalex.org/W3101686738","https://openalex.org/W3120254694","https://openalex.org/W3121675905","https://openalex.org/W3122485362","https://openalex.org/W3127854150","https://openalex.org/W3129736740","https://openalex.org/W3130706049","https://openalex.org/W3141863997","https://openalex.org/W3167350281","https://openalex.org/W3170953471","https://openalex.org/W3184432724","https://openalex.org/W4205315587","https://openalex.org/W4232108452","https://openalex.org/W4234721519","https://openalex.org/W4237504351","https://openalex.org/W4239696231","https://openalex.org/W4240119221","https://openalex.org/W4242361212","https://openalex.org/W4244275182","https://openalex.org/W4250280589","https://openalex.org/W4252801674","https://openalex.org/W4255654664","https://openalex.org/W4281672696","https://openalex.org/W4313136739","https://openalex.org/W4321128544","https://openalex.org/W4379538553","https://openalex.org/W4384831806","https://openalex.org/W4386231082","https://openalex.org/W4393234433","https://openalex.org/W4398172548","https://openalex.org/W6605785668","https://openalex.org/W6620272070","https://openalex.org/W6631309767","https://openalex.org/W6633087511","https://openalex.org/W6675011887","https://openalex.org/W6687272097","https://openalex.org/W6744110128","https://openalex.org/W6762019909","https://openalex.org/W6859419209","https://openalex.org/W7017356743"],"related_works":["https://openalex.org/W1815446007","https://openalex.org/W2783992526","https://openalex.org/W2141355868","https://openalex.org/W2032550399","https://openalex.org/W2098281589","https://openalex.org/W2057791178","https://openalex.org/W2962917430","https://openalex.org/W2970302286","https://openalex.org/W1481223916","https://openalex.org/W2732982824"],"abstract_inverted_index":{"Abstract":[0],"The":[1,101],"traveling":[2],"salesman":[3],"(or":[4],"salesperson)":[5],"problem,":[6],"short":[7],"TSP,":[8,82],"is":[9,106],"of":[10,103,128,165],"strong":[11],"interest":[12],"to":[13,133,176],"many":[14],"researchers":[15],"from":[16],"mathematics,":[17],"economics,":[18],"and":[19,31,40,62,95,119,125,146,162,181,194],"computer":[20],"science.":[21],"Manifold":[22],"TSP":[23,67,91,129,136],"variants":[24,68,153],"occur":[25],"in":[26],"nearly":[27],"every":[28,47],"scientific":[29],"field":[30],"application":[32],"domain:":[33],"e.g.,":[34],"engineering,":[35],"physics,":[36],"biology,":[37],"life":[38],"sciences,":[39],"manufacturing.":[41],"Several":[42],"thousand":[43],"papers":[44],"are":[45],"published":[46],"year.":[48],"This":[49,172],"paper":[50],"provides":[51],"the":[52,57,71,107,123,142,150,158,178,182],"first":[53,159],"systematic":[54],"survey":[55,105],"on":[56],"best":[58],"currently":[59],"known":[60],"approximability":[61,166,179],"inapproximability":[63],"results":[64,167,187,195],"for":[65,122],"well-known":[66],"such":[69],"as":[70,115],"\u201cstandard\u201d,":[72],"Path,":[73],"Bottleneck,":[74],"Maximum":[75],"Scatter,":[76],"Generalized,":[77],"Clustered,":[78],"Quota,":[79],"Prize-Collecting,":[80],"Time-dependent":[81],"Traveling":[83],"Purchaser":[84],"Problem,":[85,88,90],"Profitable":[86],"Tour":[87],"Orienteering":[89,96],"with":[92,98],"Time":[93,99],"Windows,":[94],"Problem":[97],"Windows.":[100],"foundation":[102],"our":[104],"definition":[108,127],"scheme":[109],"TSP-T3CO":[110,132,170],",":[111],"which":[112,185],"we":[113],"propose":[114],"a":[116,135],"uniform,":[117],"easy-to-use":[118],"extensible":[120],"means":[121],"formal":[124],"precise":[126],"variants.":[130],"Applying":[131],"define":[134],"variant":[137,145],"reveals":[138],"subtle":[139],"differences":[140,151],"within":[141],"same":[143],"named":[144],"also":[147],"brings":[148],"out":[149],"between":[152],"more":[154,192,199],"clearly.":[155],"We":[156],"achieve":[157],"comprehensive,":[160],"concise,":[161],"compact":[163],"representation":[164],"by":[168],"using":[169],"definitions.":[171],"makes":[173],"it":[174],"easier":[175],"understand":[177],"landscape":[180],"assumptions":[183],"under":[184],"certain":[186],"hold.":[188],"Open":[189],"gaps":[190],"become":[191],"evident":[193],"can":[196],"be":[197],"compared":[198],"easily.":[200],"Graphical":[201],"abstract":[202]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-07-02T00:00:00"}
