{"id":"https://openalex.org/W2089841750","doi":"https://doi.org/10.1137/s0097539792226771","title":"A Priori Bounds on the Euclidean Traveling Salesman","display_name":"A Priori Bounds on the Euclidean Traveling Salesman","publication_year":1995,"publication_date":"1995-06-01","ids":{"openalex":"https://openalex.org/W2089841750","doi":"https://doi.org/10.1137/s0097539792226771","mag":"2089841750"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539792226771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792226771","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/A5003269193","display_name":"Timothy Law Snyder","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Timothy Law Snyder","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086090227","display_name":"John Steele","orcid":"https://orcid.org/0000-0001-5507-5796"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Michael Steele","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003269193"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3749,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63949843,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"24","issue":"3","first_page":"665","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9884999990463257,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9800000190734863,"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/combinatorics","display_name":"Combinatorics","score":0.8316965699195862},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.778913140296936},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7391691207885742},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.6290938854217529},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5104893445968628},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.48709750175476074},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4856952130794525},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.47429612278938293},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.46104687452316284},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42154741287231445},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09691423177719116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07946401834487915},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.068398118019104}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8316965699195862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.778913140296936},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7391691207885742},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.6290938854217529},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5104893445968628},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.48709750175476074},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4856952130794525},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.47429612278938293},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.46104687452316284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42154741287231445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09691423177719116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07946401834487915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.068398118019104},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539792226771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792226771","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:repository.upenn.edu:oid_papers-1049","is_oa":false,"landing_page_url":"https://repository.upenn.edu/oid_papers/258","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Operations, Information and Decisions Papers","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.696.7715","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.696.7715","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-stat.wharton.upenn.edu/%7Esteele/Publications/PDF/SteeleSnyder95.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1975224834","https://openalex.org/W2011240422","https://openalex.org/W2033010474","https://openalex.org/W2058312407","https://openalex.org/W2081541119","https://openalex.org/W2107102056","https://openalex.org/W2151977393","https://openalex.org/W4246380588"],"related_works":["https://openalex.org/W3161375928","https://openalex.org/W222989450","https://openalex.org/W2022929595","https://openalex.org/W2798172748","https://openalex.org/W2030428607","https://openalex.org/W1662501275","https://openalex.org/W4301378414","https://openalex.org/W2949900893","https://openalex.org/W2296398547","https://openalex.org/W2110938502"],"abstract_inverted_index":{"It":[0],"is":[1,42,60,77,117,123,164],"proved":[2],"that":[3,12,142],"there":[4,143],"are":[5,86,106],"constants":[6],"$c_{1}$,":[7],"$c_{2}$,":[8],"and":[9,24,64,83,134],"$c_{3}$":[10],"such":[11,120],"for":[13,25,157],"any":[14,26,72],"set":[15],"S":[16,31,149],"of":[17,30,34,36,40,51,68,71,75,88,91,111,129,148,161,167],"n":[18],"points":[19,92],"in":[20,58,93,115,126],"the":[21,32,37,49,66,89,112,127,130,159],"unit":[22],"square":[23],"minimum-length":[27],"tour":[28,147],"T":[29,41,59,76],"sum":[33,67,160],"squares":[35],"edge":[38,69],"lengths":[39,70],"bounded":[43,78,165],"by":[44,79],"$c_{1}":[45],"\\log":[46],"n$.":[47],"(2)":[48],"number":[50,90],"edges":[52,163],"having":[53],"length":[54],"t":[55],"or":[56],"greater":[57],"at":[61],"most":[62],"$c_{2}/t^{2}$,":[63],"(3)":[65],"subset":[73],"E":[74],"$c_{3}|E|^{1/2}$.":[80],"The":[81,109],"second":[82],"third":[84],"bounds":[85],"independent":[87],"S,":[94],"as":[95,97],"well":[96],"their":[98],"locations.":[99],"Extensions":[100],"to":[101],"dimensions":[102],"$d":[103],">":[104],"2$":[105],"also":[107],"sketched.":[108],"presence":[110],"logarithmic":[113],"term":[114,122],"(1)":[116],"engaging":[118],"because":[119],"a":[121],"not":[124,153],"needed":[125],"case":[128],"minimum":[131],"spanning":[132],"tree":[133],"several":[135],"analogous":[136],"problems,":[137],"and,":[138],"furthermore,":[139],"we":[140],"know":[141],"always":[144],"exists":[145],"some":[146],"(which":[150],"perhaps":[151],"does":[152],"have":[154],"minimal":[155],"length)":[156],"which":[158],"squared":[162],"independently":[166],"n.":[168]},"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}