{"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":"https://link.springer.com/content/pdf/10.1007/s00453-025-01309-9.pdf","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://link.springer.com/content/pdf/10.1007/s00453-025-01309-9.pdf","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":false,"raw_author_name":"Bodo Manthey","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Enschede, The Netherlands"],"raw_orcid":null,"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":true,"raw_author_name":"Jesse van Rhijn","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Enschede, The Netherlands"],"raw_orcid":null,"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":1,"corresponding_author_ids":["https://openalex.org/A5059117885"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.6115,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61937764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"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":"https://link.springer.com/content/pdf/10.1007/s00453-025-01309-9.pdf","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":true,"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/article"}],"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":"https://link.springer.com/content/pdf/10.1007/s00453-025-01309-9.pdf","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":"Rigorous Analysis of Local Search","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409341537.pdf","grobid_xml":"https://content.openalex.org/works/W4409341537.grobid-xml"},"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":{"Abstract":[0],"The":[1,131],"2-opt":[2,231],"heuristic":[3,9],"is":[4,27,211],"a":[5,156],"simple":[6],"local":[7],"search":[8],"for":[10,64,118,135,201,208,229],"the":[11,30,58,65,70,92,97,194,220],"travelling":[12],"salesperson":[13],"problem":[14],"(TSP).":[15],"Although":[16],"it":[17],"usually":[18],"performs":[19],"well":[20],"in":[21,29,47,57,68,89,172,190],"practice,":[22],"its":[23],"worst-case":[24],"running":[25],"time":[26],"exponential":[28],"number":[31],"of":[32,61],"cities.":[33],"Attempts":[34],"to":[35,164],"reconcile":[36],"this":[37,216],"difference":[38],"between":[39],"practice":[40],"and":[41,81,96,152,174,188],"theory":[42],"have":[43],"used":[44,78,155],"smoothed":[45,62,85,226],"analysis,":[46],"which":[48,69,160],"adversarial":[49],"instances":[50],"are":[51,55,72],"perturbed":[52],"probabilistically.":[53],"We":[54],"interested":[56],"classical":[59],"model":[60,75,159,168],"analysis":[63,115,134,199],"Euclidean":[66,230],"TSP,":[67],"perturbations":[71,203],"Gaussian.":[73],"This":[74],"was":[76,147],"previously":[77],"by":[79,149],"Manthey":[80],"Veenstra,":[82],"who":[83,154],"obtained":[84],"complexity":[86,227],"bounds":[87,170,207,228],"polynomial":[88,171,206],"n":[90,173],",":[91,95,187],"dimension":[93],"d":[94,191,210],"perturbation":[98,158],"strength":[99],"$$\\sigma":[100,175],"^{-1}$$":[101],"<mml:math":[102,122,139,177],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[103,123,140,178],"<mml:msup>":[104,179],"<mml:mi>\u03c3</mml:mi>":[105,180],"<mml:mrow>":[106,124,141,181],"<mml:mo>-</mml:mo>":[107,182],"<mml:mn>1</mml:mn>":[108],"</mml:mrow>":[109,128,145,184],"</mml:msup>":[110,185],"</mml:math>":[111,129,146,186],".":[112,130,192],"However,":[113],"their":[114],"only":[116,132],"works":[117],"$$d":[119,136],"\\ge":[120],"4$$":[121],"<mml:mi>d</mml:mi>":[125,142,183],"<mml:mo>\u2265</mml:mo>":[126],"<mml:mn>4</mml:mn>":[127],"previous":[133],"\\le":[137],"3$$":[138],"<mml:mo>\u2264</mml:mo>":[143],"<mml:mn>3</mml:mn>":[144],"performed":[148],"Englert,":[150],"R\u00f6glin":[151],"V\u00f6cking,":[153],"different":[157],"can":[161],"be":[162],"translated":[163],"Gaussian":[165,202,233],"perturbations.":[166,234],"Their":[167],"yields":[169,205],"^{-d}$$":[176],"super-exponential":[189],"As":[193],"fact":[195],"that":[196,204],"no":[197],"direct":[198],"exists":[200],"all":[209,224],"somewhat":[212],"unsatisfactory,":[213],"we":[214,222],"perform":[215],"missing":[217],"analysis.":[218],"Along":[219],"way,":[221],"improve":[223],"existing":[225],"with":[232]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}