{"id":"https://openalex.org/W1485858170","doi":"https://doi.org/10.1137/s0097539701391518","title":"The probabilistic relationship between the assignment and travelling salesman problems","display_name":"The probabilistic relationship between the assignment and travelling salesman problems","publication_year":2006,"publication_date":"2006-12-01","ids":{"openalex":"https://openalex.org/W1485858170","doi":"https://doi.org/10.1137/s0097539701391518","mag":"1485858170"},"language":"en","primary_location":{"id":"pmh:oai:researchonline.lse.ac.uk:35445","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-4935-7820>","pdf_url":null,"source":{"id":"https://openalex.org/S4306400050","display_name":"London School of Economics and Political Science Theses Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":[],"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/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan Frieze","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8481-5615","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083890565","display_name":"Gregory B. Sorkin","orcid":"https://orcid.org/0000-0003-4935-7820"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gregory B. Sorkin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4935-7820","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06574865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9983999729156494,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.995199978351593,"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":0.8707973957061768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7854771614074707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6870776414871216},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6202703714370728},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5834975242614746},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5538759827613831},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4932858347892761},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47712230682373047},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4672401249408722},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.4665714502334595},{"id":"https://openalex.org/keywords/assignment-problem","display_name":"Assignment problem","score":0.4524369239807129},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4482118785381317},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42278367280960083},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3126644492149353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1510961353778839},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07912307977676392},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07704058289527893}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8707973957061768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7854771614074707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6870776414871216},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6202703714370728},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5834975242614746},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5538759827613831},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4932858347892761},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47712230682373047},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4672401249408722},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.4665714502334595},{"id":"https://openalex.org/C85044808","wikidata":"https://www.wikidata.org/wiki/Q620614","display_name":"Assignment problem","level":2,"score":0.4524369239807129},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4482118785381317},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42278367280960083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3126644492149353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1510961353778839},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07912307977676392},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07704058289527893},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:researchonline.lse.ac.uk:35445","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-4935-7820>","pdf_url":null,"source":{"id":"https://openalex.org/S4306400050","display_name":"London School of Economics and Political Science Theses Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:eprints.lse.ac.uk:35445","is_oa":false,"landing_page_url":"http://epubs.siam.org/sicomp/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"mag:1485858170","is_oa":false,"landing_page_url":"http://eprints.lse.ac.uk/35445/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2035337703","https://openalex.org/W2063112592","https://openalex.org/W2089060318","https://openalex.org/W2105684878","https://openalex.org/W1552320966","https://openalex.org/W2028378628","https://openalex.org/W2604874681","https://openalex.org/W1780193764","https://openalex.org/W76887364","https://openalex.org/W2010944042","https://openalex.org/W2275930697","https://openalex.org/W1497071043","https://openalex.org/W2065154034","https://openalex.org/W1599707802","https://openalex.org/W1523833456","https://openalex.org/W1974139762","https://openalex.org/W1850832643","https://openalex.org/W2010260400","https://openalex.org/W2144398243","https://openalex.org/W2996602723"],"abstract_inverted_index":{"We":[0],"consider":[1,115],"the":[2,5,21,35,50,63,70,87,110,116,120],"gap":[3,51,90,118],"between":[4,119],"cost":[6,22],"of":[7,23,62,65,86],"an":[8,24,40,75,92],"optimal":[9,25,76,121],"assignment":[10,77],"in":[11,29,74],"a":[12,30,101],"complete":[13,31],"bipartite":[14],"graph":[15,33],"with":[16,34,47,96],"random":[17,102],"edge":[18,37,72],"weights,":[19],"and":[20,55,122,130],"traveling":[26,104],"salesman":[27,105],"tour":[28],"directed":[32],"same":[36],"weights.":[38],"Using":[39],"improved":[41],"\u201cpatching\u201d":[42],"heuristic,":[43],"we":[44,113],"show":[45],"that":[46,56,69],"high":[48,97],"probability":[49],"is":[52,59,68,91,126],"$O((\\ln":[53],"n)^2/n)$,":[54],"its":[57],"expectation":[58,79],"$\\Omega(1/n)$.":[60],"One":[61],"underpinnings":[64],"this":[66],"result":[67],"largest":[71],"weight":[73],"has":[78],"$\\Theta(\\ln":[80],"n":[81],"/":[82],"n)$.":[83],"A":[84],"consequence":[85],"small":[88],"assignment\u2013TSP":[89,111],"$e^{\\tilde{O}(\\sqrt{n})}$\u2010time":[93],"algorithm":[94],"which,":[95],"probability,":[98],"exactly":[99],"solves":[100],"asymmetric":[103],"instance.":[106],"In":[107],"addition":[108],"to":[109],"gap,":[112],"also":[114],"expected":[117],"second\u2010best":[123],"assignments;":[124],"it":[125],"at":[127,131],"least":[128],"$\\Omega(1/n^2)$":[129],"most":[132],"$O(\\ln":[133],"n/n^2)$.":[134]},"counts_by_year":[],"updated_date":"2025-11-06T04:12:42.849631","created_date":"2025-10-10T00:00:00"}
