{"id":"https://openalex.org/W4406184077","doi":"https://doi.org/10.1155/cplx/3672180","title":"Counter\u2010Example to Diaby\u2019s et al. Linear Programming Solution to the Traveling Salesman Problem","display_name":"Counter\u2010Example to Diaby\u2019s et al. Linear Programming Solution to the Traveling Salesman Problem","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4406184077","doi":"https://doi.org/10.1155/cplx/3672180"},"language":"en","primary_location":{"id":"doi:10.1155/cplx/3672180","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/3672180","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/3672180","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/3672180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003343893","display_name":"Rados\u0142aw Hofman","orcid":"https://orcid.org/0000-0001-5693-8151"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rados\u0142aw Hofman","raw_affiliation_strings":["Independent Researcher ,  Poznan\u0301 ,  Poland","Independent Researcher ,  Pozna\u0144 ,  Poland"],"raw_orcid":"https://orcid.org/0000-0001-5693-8151","affiliations":[{"raw_affiliation_string":"Independent Researcher ,  Poznan\u0301 ,  Poland","institution_ids":[]},{"raw_affiliation_string":"Independent Researcher ,  Pozna\u0144 ,  Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5003343893"],"corresponding_institution_ids":[],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00428792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.991100013256073,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9898999929428101,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.8600540161132812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5202214121818542},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5047975778579712},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4955407381057739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3655858635902405}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8600540161132812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5202214121818542},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5047975778579712},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4955407381057739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3655858635902405}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/cplx/3672180","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/3672180","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/3672180","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1ce6a6f4891a40679f05677805742eef","is_oa":true,"landing_page_url":"https://doaj.org/article/1ce6a6f4891a40679f05677805742eef","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/cplx/3672180","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/3672180","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/3672180","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406184077.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1973490548","https://openalex.org/W2000432016","https://openalex.org/W2036265926","https://openalex.org/W2042599036","https://openalex.org/W2065547308","https://openalex.org/W2080276486","https://openalex.org/W2158834265","https://openalex.org/W4231244924","https://openalex.org/W4285591713"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1525389557","https://openalex.org/W2361554335","https://openalex.org/W2164188042","https://openalex.org/W2359992618","https://openalex.org/W1979597421","https://openalex.org/W4306878646","https://openalex.org/W2495211334"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"a":[3,9,76],"method":[4],"of":[5,46],"constructing":[6],"counter\u2010examples":[7],"and":[8,59,79],"complete":[10],"counter\u2010example":[11,28,68,74,100],"to":[12,18,22,42,84,119],"the":[13,20,23,32,47,51,67,80,89,94,112,123],"linear":[14],"programming":[15],"model":[16,33,52],"alleged":[17],"be":[19],"solution":[21],"traveling":[24],"salesman":[25],"problem.":[26,49],"The":[27,72,99],"is":[29,75],"checked":[30],"against":[31],"proposed":[34],"by":[35],"Diaby":[36],"et":[37],"al.":[38],"However,":[39],"it":[40],"applies":[41],"all":[43],"similar":[44],"formulations":[45],"TSP":[48],"Although":[50],"in":[53,57,105,122],"question":[54],"was":[55,69,82,96],"published":[56],"2006,":[58],"there":[60],"were":[61],"several":[62],"discussions":[63],"regarding":[64],"its":[65],"correctness,":[66],"never":[70],"presented.":[71],"presented":[73],"regular":[77],"graph,":[78],"aim":[81],"not":[83],"have":[85],"an":[86],"example":[87],"with":[88],"least":[90],"possible":[91],"size;":[92],"therefore,":[93,102],"focus":[95],"on":[97],"clarity.":[98],"has,":[101],"366":[103],"nodes":[104,121],"two":[106],"main":[107,113],"clusters,":[108],"each":[109],"node":[110],"(in":[111],"part)":[114],"having":[115],"exactly":[116],"four":[117],"connections":[118],"other":[120],"cluster.":[124]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
