{"id":"https://openalex.org/W4409341537","doi":"https://doi.org/10.1007/s00453-025-01309-9","title":"Improved Smoothed Analysis of 2-Opt for the Euclidean TSP","display_name":"Improved Smoothed Analysis of 2-Opt for the Euclidean TSP","publication_year":2025,"publication_date":"2025-04-10","ids":{"openalex":"https://openalex.org/W4409341537","doi":"https://doi.org/10.1007/s00453-025-01309-9","pmid":"https://pubmed.ncbi.nlm.nih.gov/40786622"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-025-01309-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01309-9","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s00453-025-01309-9","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002315999","display_name":"Bodo Manthey","orcid":"https://orcid.org/0000-0001-6278-5059"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Bodo Manthey","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Enschede, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059117885","display_name":"Jesse van Rhijn","orcid":"https://orcid.org/0000-0002-3416-7672"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jesse van Rhijn","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Enschede, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002315999"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.343,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.80455338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"87","issue":"7","first_page":"1008","last_page":"1039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10232","display_name":"Optical Network Technologies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10232","display_name":"Optical Network Technologies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10847","display_name":"Advanced Optical Network Technologies","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10767","display_name":"Advanced Photonic Communication Systems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/theory-of-computation","display_name":"Theory of computation","score":0.604810893535614},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5528804063796997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48817282915115356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48039963841438293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4034711420536041},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32887351512908936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30698683857917786},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15670865774154663}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.604810893535614},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5528804063796997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48817282915115356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48039963841438293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4034711420536041},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32887351512908936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30698683857917786},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15670865774154663}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-025-01309-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01309-9","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},{"id":"pmid:40786622","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40786622","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:12334457","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12334457","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12334457/pdf/453_2025_Article_1309.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Algorithmica","raw_type":"Text"},{"id":"pmh:oai:ris.utwente.nl:openaire_cris_publications/8aab3a86-c7fa-4885-996c-fb2239132f8f","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/8aab3a86-c7fa-4885-996c-fb2239132f8f","pdf_url":"https://ris.utwente.nl/ws/files/499132514/s00453-025-01309-9.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":"Manthey, B & van Rhijn, J 2025, 'Improved Smoothed Analysis of 2-Opt for the Euclidean TSP', Algorithmica, vol. 87, no. 7, pp. 1008-1039. https://doi.org/10.1007/s00453-025-01309-9","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00453-025-01309-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01309-9","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1658578737","display_name":null,"funder_award_id":"OCENW.KLEIN.176","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1552810675","https://openalex.org/W1923505183","https://openalex.org/W1982562599","https://openalex.org/W1991567646","https://openalex.org/W2034053794","https://openalex.org/W2042851446","https://openalex.org/W2055569927","https://openalex.org/W2057795374","https://openalex.org/W2079868147","https://openalex.org/W2144476828","https://openalex.org/W2519455498","https://openalex.org/W2998757566","https://openalex.org/W4210501458","https://openalex.org/W4233497604","https://openalex.org/W4300005723","https://openalex.org/W4300223101","https://openalex.org/W6602606630"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4409439182","https://openalex.org/W2053286651","https://openalex.org/W2980963558","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378"],"abstract_inverted_index":{"The":[0,116],"2-opt":[1,203],"heuristic":[2,8],"is":[3,26,183],"a":[4,135],"simple":[5],"local":[6],"search":[7],"for":[9,63,109,120,173,180,201],"the":[10,29,57,64,69,90,94,166,192],"travelling":[11],"salesperson":[12],"problem":[13],"(TSP).":[14],"Although":[15],"it":[16],"usually":[17],"performs":[18],"well":[19],"in":[20,28,46,56,67,88,151,163],"practice,":[21],"its":[22],"worst-case":[23],"running":[24],"time":[25],"exponential":[27],"number":[30],"of":[31,60],"cities.":[32],"Attempts":[33],"to":[34,143],"reconcile":[35],"this":[36,188],"difference":[37],"between":[38],"practice":[39],"and":[40,80,93,131,153,161],"theory":[41],"have":[42],"used":[43,77,134],"smoothed":[44,61,84,198],"analysis,":[45],"which":[47,68,139],"adversarial":[48],"instances":[49],"are":[50,54,71],"perturbed":[51],"probabilistically.":[52],"We":[53],"interested":[55],"classical":[58],"model":[59,74,138,147],"analysis":[62,106,119,171],"Euclidean":[65,202],"TSP,":[66],"perturbations":[70,175],"Gaussian.":[72],"This":[73],"was":[75,126],"previously":[76],"by":[78,128],"Manthey":[79],"Veenstra,":[81],"who":[82,133],"obtained":[83],"complexity":[85,199],"bounds":[86,149,179,200],"polynomial":[87,150,178],"<i>n</i>,":[89],"dimension":[91],"<i>d</i>,":[92],"perturbation":[95,137],"strength":[96],"<mml:math":[97,110,121,154],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>\u03c3</mml:mi>":[98,155],"<mml:mrow><mml:mo>-</mml:mo>":[99,156],"<mml:mn>1</mml:mn></mml:mrow>":[100],"</mml:msup>":[101,158],"</mml:math>":[102,114,125,159],".":[103,115],"However,":[104],"their":[105],"only":[107,117],"works":[108],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>d</mml:mi>":[111,122],"<mml:mo>\u2265</mml:mo>":[112],"<mml:mn>4</mml:mn></mml:mrow>":[113],"previous":[118],"<mml:mo>\u2264</mml:mo>":[123],"<mml:mn>3</mml:mn></mml:mrow>":[124],"performed":[127],"Englert,":[129],"R\u00f6glin":[130],"V\u00f6cking,":[132],"different":[136],"can":[140],"be":[141],"translated":[142],"Gaussian":[144,174,205],"perturbations.":[145,206],"Their":[146],"yields":[148,177],"<i>n</i>":[152],"<mml:mi>d</mml:mi></mml:mrow>":[157],",":[160],"super-exponential":[162],"<i>d</i>.":[164],"As":[165],"fact":[167],"that":[168,176],"no":[169],"direct":[170],"exists":[172],"all":[181,196],"<i>d</i>":[182],"somewhat":[184],"unsatisfactory,":[185],"we":[186,194],"perform":[187],"missing":[189],"analysis.":[190],"Along":[191],"way,":[193],"improve":[195],"existing":[197],"with":[204]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
