{"id":"https://openalex.org/W1986948282","doi":"https://doi.org/10.1137/090749396","title":"Approximating TSP on Metrics with Bounded Global Growth","display_name":"Approximating TSP on Metrics with Bounded Global Growth","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1986948282","doi":"https://doi.org/10.1137/090749396","mag":"1986948282"},"language":"en","primary_location":{"id":"doi:10.1137/090749396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090749396","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/A5018708584","display_name":"T-H. Hubert Chan","orcid":"https://orcid.org/0000-0002-8340-235X"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"T.-H. Hubert Chan","raw_affiliation_strings":["Department of Computer Science, The University of Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078381067","display_name":"Anupam Gupta","orcid":"https://orcid.org/0000-0001-5579-3405"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anupam Gupta","raw_affiliation_strings":["Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078381067"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.3242,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.59747949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"3","first_page":"587","last_page":"617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9350000023841858,"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/dimension","display_name":"Dimension (graph theory)","score":0.7407976388931274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7363848686218262},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7324862480163574},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.6593970060348511},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6284497380256653},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6246122121810913},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5503368973731995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.458459734916687},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4454953670501709},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.43738508224487305},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.41472500562667847},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19857874512672424},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0944623053073883},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08378753066062927}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7407976388931274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7363848686218262},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7324862480163574},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.6593970060348511},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6284497380256653},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6246122121810913},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5503368973731995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.458459734916687},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4454953670501709},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.43738508224487305},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.41472500562667847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19857874512672424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0944623053073883},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08378753066062927},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/090749396","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090749396","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.141.6728","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.6728","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~anupamg/papers/net_cd.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.362.8048","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.362.8048","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.649.5129","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.5129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:repository.cmu.edu:compsci-1826","is_oa":false,"landing_page_url":"http://repository.cmu.edu/compsci/823","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science Department","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/160535","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/160535","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4702511812","display_name":"CAREER:    Algorithmic Theory and Applications of Metric Emeddings","funder_award_id":"0448095","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6484169224","display_name":"ITR/SY+IM+AP: Center for Applied Algorithms","funder_award_id":"0122581","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1983067644","https://openalex.org/W1991755800","https://openalex.org/W1994248285","https://openalex.org/W2002041206","https://openalex.org/W2007279610","https://openalex.org/W2014411916","https://openalex.org/W2029401646","https://openalex.org/W2107342718","https://openalex.org/W2114585066","https://openalex.org/W2141355868","https://openalex.org/W2165142526","https://openalex.org/W2169840105","https://openalex.org/W2583644876","https://openalex.org/W3030774092","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W2008939113","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W37157938","https://openalex.org/W4298154183"],"abstract_inverted_index":{"The":[0],"traveling":[1],"salesman":[2],"problem":[3,9,171],"(TSP)":[4],"is":[5,11,80,172],"a":[6,71,99,131,139,184],"canonical":[7],"NP-complete":[8],"which":[10,168],"proved":[12],"by":[13],"Trevisan":[14],"[SIAM":[15],"J.":[16],"Comput.,":[17],"30":[18],"(2000),":[19],"pp.":[20],"475--485]":[21],"to":[22,58,91,174,176,180,193,221],"be":[23,92],"MAX-SNP":[24],"hard":[25,173],"even":[26],"on":[27,61,167],"high-dimensional":[28],"Euclidean":[29],"metrics.":[30],"To":[31],"circumvent":[32],"this":[33,95],"hardness,":[34],"researchers":[35],"have":[36,216,225],"been":[37],"developing":[38],"approximation":[39],"schemes":[40],"for":[41,150,201],"\u201esimpler\u201d":[42],"instances":[43],"of":[44,51,54,67,73,77,102,109,127,164,187,196],"the":[45,49,85,106,169,197],"problem.":[46],"For":[47],"instance,":[48],"algorithms":[50,190],"Arora":[52],"and":[53,199,204,224],"Talwar":[55],"show":[56,210],"how":[57],"approximate":[59,175],"TSP":[60,170],"low-dimensional":[62],"metrics":[63,123,157,163,215],"(for":[64],"different":[65],"notions":[66,76],"metric":[68,78,132],"dimension).":[69],"However,":[70],"feature":[72],"most":[74],"current":[75],"dimension":[79,103,135],"that":[81,104,124,142,211,218],"they":[82],"are":[83],"\u201elocal\u201d:":[84],"definitions":[86],"require":[87],"every":[88,151],"local":[89],"neighborhood":[90],"well-behaved.":[93],"In":[94],"paper,":[96],"we":[97,137,209],"define":[98],"global":[100,134],"notion":[101,108],"generalizes":[105],"popular":[107],"doubling":[110],"dimension,":[111],"but":[112],"still":[113],"allows":[114,121],"some":[115,122,194],"small":[116],"dense":[117],"regions;":[118],"e.g.,":[119],"it":[120],"contain":[125,162],"cliques":[126],"size":[128,165,226],"$\\sqrt{n}$.":[129],"Given":[130],"with":[133,158],"$\\dim_{C}$,":[136],"give":[138],"$(1+\\varepsilon)$-approximation":[140],"algorithm":[141],"runs":[143],"in":[144,148],"subexponential":[145],"time,":[146],"i.e.,":[147],"$\\exp(O(n^{\\delta}\\varepsilon^{-4\\dim_{C}}))$-time":[149],"constant":[152],"$0<\\delta<1$.":[153],"As":[154],"mentioned":[155],"above,":[156],"bounded":[159,214],"$\\dim_{C}$":[160],"may":[161],"$O(\\sqrt{n})$":[166],"within":[177],"$(1+\\varepsilon)$.":[178],"Hence,":[179],"do":[181],"better":[182],"than":[183],"running":[185],"time":[186],"$\\Omega(\\exp\\{\\sqrt{n}\\})$,":[188],"our":[189],"find":[191],"$O(1)$-approximations":[192],"portions":[195],"tour,":[198],"$(1+\\varepsilon)$-approximations":[200],"other":[202],"portions,":[203],"stitch":[205],"them":[206],"together.":[207],"Moreover,":[208],"such":[212],"globally":[213],"spanners":[217],"preserve":[219],"distances":[220],"arbitrary":[222],"accuracy":[223],"$\\Theta(n^{1.5})$.":[227]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
