{"id":"https://openalex.org/W2048039662","doi":"https://doi.org/10.1080/10637199708915622","title":"SOLVING THE TRAVELING SALESMAN PROBLEM USING EFFICIENT RANDOMIZED PARALLEL APPROXIMATION ALGORITHMS","display_name":"SOLVING THE TRAVELING SALESMAN PROBLEM USING EFFICIENT RANDOMIZED PARALLEL APPROXIMATION ALGORITHMS","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2048039662","doi":"https://doi.org/10.1080/10637199708915622","mag":"2048039662"},"language":"en","primary_location":{"id":"doi:10.1080/10637199708915622","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199708915622","pdf_url":null,"source":{"id":"https://openalex.org/S85375271","display_name":"International Journal of Parallel Emergent and Distributed Systems","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192","1744-5760","1744-5779"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","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/A5087894632","display_name":"Keqin Li","orcid":"https://orcid.org/0000-0001-5224-4048"},"institutions":[{"id":"https://openalex.org/I157455823","display_name":"SUNY New Paltz","ror":"https://ror.org/03j3dv688","country_code":"US","type":"education","lineage":["https://openalex.org/I157455823"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"KEQIN LI","raw_affiliation_strings":["Department of Mathematics and Computer Science, State University of New York, New Paltz, New York, 12561, USA","Department of Mathematics and Computer Science , State University of New York , New Paltz, New York, 12561, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, State University of New York, New Paltz, New York, 12561, USA","institution_ids":["https://openalex.org/I157455823"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science , State University of New York , New Paltz, New York, 12561, USA","institution_ids":["https://openalex.org/I157455823"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087894632"],"corresponding_institution_ids":["https://openalex.org/I157455823"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.21836674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"10","issue":"3-4","first_page":"271","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9994999766349792,"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":0.9994999766349792,"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/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9984999895095825,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.8406102657318115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5470134615898132},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.498720645904541},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4492708742618561},{"id":"https://openalex.org/keywords/christofides-algorithm","display_name":"Christofides algorithm","score":0.4400192201137543},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.42654505372047424},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3939782679080963}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8406102657318115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5470134615898132},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.498720645904541},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4492708742618561},{"id":"https://openalex.org/C138600008","wikidata":"https://www.wikidata.org/wiki/Q498144","display_name":"Christofides algorithm","level":4,"score":0.4400192201137543},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.42654505372047424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3939782679080963}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10637199708915622","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199708915622","pdf_url":null,"source":{"id":"https://openalex.org/S85375271","display_name":"International Journal of Parallel Emergent and Distributed Systems","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192","1744-5760","1744-5779"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W92959217","https://openalex.org/W244644848","https://openalex.org/W1513400187","https://openalex.org/W1655990431","https://openalex.org/W1969186119","https://openalex.org/W1977119258","https://openalex.org/W1981234161","https://openalex.org/W1995040285","https://openalex.org/W2006060626","https://openalex.org/W2011594074","https://openalex.org/W2022179164","https://openalex.org/W2033887412","https://openalex.org/W2042986967","https://openalex.org/W2053913299","https://openalex.org/W2055336889","https://openalex.org/W2055370404","https://openalex.org/W2069323107","https://openalex.org/W2069446854","https://openalex.org/W2074276908","https://openalex.org/W2086917808","https://openalex.org/W2117226423","https://openalex.org/W2120490947","https://openalex.org/W2123241324","https://openalex.org/W2132806150","https://openalex.org/W2324108981","https://openalex.org/W2610479830","https://openalex.org/W2956015669","https://openalex.org/W4210697874"],"related_works":["https://openalex.org/W4200179302","https://openalex.org/W1595757466","https://openalex.org/W4389782626","https://openalex.org/W2766731260","https://openalex.org/W3210931532","https://openalex.org/W2620231896","https://openalex.org/W1645834615","https://openalex.org/W87675801","https://openalex.org/W2171568915","https://openalex.org/W2055574289"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"combine":[4],"the":[5,14,20,54,57,66,159,162,221],"techniques":[6],"of":[7,19,56,68,161,233],"approximation,":[8],"parallelism,":[9],"and":[10,63,79,150,208],"randomization":[11],"to":[12,218],"solve":[13,220],"traveling":[15,118,192],"salesman":[16,119,193],"problem,":[17],"one":[18],"most":[21],"celebrated":[22],"problems":[23],"in":[24,168],"computer":[25],"science.":[26],"We":[27,170],"show":[28,172],"that":[29,39,93,122,173,196],"there":[30,100,174],"is":[31,53,65,85,101,138,158,175,216],"an":[32,69],"EREW":[33],"PRAM":[34,89,106,180],"algorithm":[35,73,90,107,144,181],"A":[36,40,51,61,91,108,123,182,197],"1":[37,131],"such":[38,121,195],"1(l)":[41,52],"\u2264":[42,125,199],"2":[43,92],"OPT(l)":[44,64],"for":[45,111,185],"all":[46,112,166,186],"TSP":[47,113,187,222],"instances":[48,114,188],"l,":[49,115,189],"where":[50,136,156],"length":[55,67,160],"tour":[58,194],"produced":[59],"by":[60,228],"1,":[62],"optimum":[70],"tour.":[71],"The":[72,142],"has":[74,145],"time":[75,146,204],"complexity":[76,147,205],"O(log2":[77,148,206],"n),":[78,149,207],"uses":[80,94,151],"O(n":[81,95,152,210],"2)":[82],"processors.":[83,98,213],"There":[84],"a":[86,102,117,176,191,230],"similar":[87],"CREW":[88,105,179],"2/log2":[96],"n)":[97],"Furthermore,":[99],"Monte":[103],"Carlo":[104],"3":[109],"which,":[110,184],"finds":[116],"lour":[120],"3(l)":[124],"1.5OPT(l)":[126],"with":[127,202,225],"probability":[128,227],"at":[129],"least":[130],"\u2212":[132],"(1/2":[133],"k":[134,137],"),":[135],"any":[139],"large":[140],"integer.":[141],"randomized":[143],"5.5":[153,211],"L)":[154,212],"processors,":[155],"L":[157],"interval":[163],"which":[164],"contains":[165],"distances":[167],"l.":[169],"also":[171],"Las":[177],"Vegas":[178],"4":[183],"produces":[190],"4(l)":[198],"1.5":[200],"OPT(l),":[201],"expected":[203],"using":[209,229],"Therefore,":[214],"it":[215],"possible":[217],"accurately":[219],"very":[223],"fast":[224],"high":[226],"reasonable":[231],"amount":[232],"resources.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}