{"id":"https://openalex.org/W2167197687","doi":"https://doi.org/10.1145/1082036.1082041","title":"Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs","display_name":"Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2167197687","doi":"https://doi.org/10.1145/1082036.1082041","mag":"2167197687"},"language":"en","primary_location":{"id":"doi:10.1145/1082036.1082041","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1082036.1082041","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Haim Kaplan","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012404981","display_name":"Moshe Lewenstein","orcid":"https://orcid.org/0000-0002-8272-244X"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Moshe Lewenstein","raw_affiliation_strings":["Bar-Ilan University, Ramat-Gan, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bar-Ilan University, Ramat-Gan, Israel","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067943969","display_name":"Nira Shafrir","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nira Shafrir","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111449864","display_name":"Maxim Sviridenko","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maxim Sviridenko","raw_affiliation_strings":["IBM T.J. Watson Research Center, Yorktown Heights, New York"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM T.J. Watson Research Center, Yorktown Heights, New York","institution_ids":["https://openalex.org/I4210114115"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.6242,"has_fulltext":false,"cited_by_count":179,"citation_normalized_percentile":{"value":0.9855495,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"4","first_page":"602","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9853000044822693,"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":0.9853000044822693,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9839000105857849,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9708999991416931,"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/multigraph","display_name":"Multigraph","score":0.9103445410728455},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.712634265422821},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6904298663139343},{"id":"https://openalex.org/keywords/cycle-basis","display_name":"Cycle basis","score":0.5427709817886353},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.5395651459693909},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.49118825793266296},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4629102349281311},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44364869594573975},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.41411447525024414},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.4115551710128784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36239808797836304},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.16181835532188416}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.9103445410728455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.712634265422821},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6904298663139343},{"id":"https://openalex.org/C26752605","wikidata":"https://www.wikidata.org/wiki/Q16766188","display_name":"Cycle basis","level":5,"score":0.5427709817886353},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.5395651459693909},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.49118825793266296},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4629102349281311},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44364869594573975},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.41411447525024414},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.4115551710128784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36239808797836304},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.16181835532188416},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1082036.1082041","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1082036.1082041","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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":31,"referenced_works":["https://openalex.org/W107646379","https://openalex.org/W1482447760","https://openalex.org/W1488861257","https://openalex.org/W1490932874","https://openalex.org/W1521148214","https://openalex.org/W1553729051","https://openalex.org/W1915280757","https://openalex.org/W1977006915","https://openalex.org/W1989048084","https://openalex.org/W2008217702","https://openalex.org/W2009803313","https://openalex.org/W2017314050","https://openalex.org/W2021625223","https://openalex.org/W2033530135","https://openalex.org/W2035610952","https://openalex.org/W2037050365","https://openalex.org/W2052352992","https://openalex.org/W2058748455","https://openalex.org/W2061753037","https://openalex.org/W2080721852","https://openalex.org/W2090223576","https://openalex.org/W2101468281","https://openalex.org/W2102403605","https://openalex.org/W2102706148","https://openalex.org/W2117226423","https://openalex.org/W2130200244","https://openalex.org/W2134761228","https://openalex.org/W2141355868","https://openalex.org/W2152453230","https://openalex.org/W2769376643","https://openalex.org/W2914372558"],"related_works":["https://openalex.org/W4300697888","https://openalex.org/W4241541331","https://openalex.org/W2952621743","https://openalex.org/W2769159583","https://openalex.org/W2016168023","https://openalex.org/W2259723333","https://openalex.org/W4381707782","https://openalex.org/W2896710021","https://openalex.org/W2963726052","https://openalex.org/W1002323541"],"abstract_inverted_index":{"A":[0],"directed":[1],"multigraph":[2,29,53],"is":[3,17,94,120,207,250,301],"said":[4],"to":[5,101,136,196,235,289],"be":[6],"d":[7,19,51],"-regular":[8,52],"if":[9,49],"the":[10,50,123,157,168,186,189,201,212,215,221,236,246,255,261,277,280,330],"indegree":[11],"and":[12,96,344],"outdegree":[13],"of":[14,33,63,77,89,115,126,152,156,167,188,211,214,279,294,321,329],"every":[15],"vertex":[16],"exactly":[18],".":[20,326],"By":[21],"Hall's":[22],"theorem,":[23],"one":[24,87,111],"can":[25,68],"represent":[26],"such":[27,103,112,140],"a":[28,31,70,98,104,113,138,149,179,198,226,230,242,270,297,314],"as":[30],"combination":[32],"at":[34,85,121,183,208,274,302],"most":[35,86,275,303],"n":[36,74,307,325],"2":[37,75,202,306,324],"cycle":[38,78,116,173,203,266,295],"covers,":[39,204,267],"each":[40,81,90],"taken":[41],"with":[42,181,225,272,318,348],"an":[43,132,153],"appropriate":[44],"multiplicity.":[45],"We":[46],"prove":[47],"that":[48,175],"does":[54],"not":[55,177,268],"contain":[56],"more":[57],"than":[58,254,309],"\u230a":[59],"d/2":[60],"\u230b":[61],"copies":[62],"any":[64],"2-cycle":[65,82,180],"then":[66,144,286],"we":[67,129,193,240,285],"find":[69,102],"similar":[71],"decomposition":[72],"into":[73],"pairs":[76],"covers":[79,117,174,296],"where":[80],"occurs":[83],"in":[84,147],"component":[88],"pair.":[91],"Our":[92],"proof":[93],"constructive":[95],"gives":[97,264],"polynomial":[99],"algorithm":[100,135,244,317],"decomposition.":[105],"Since":[106],"our":[107],"applications":[108,328],"only":[109],"need":[110],"pair":[114,293],"whose":[118,205,299],"weight":[119,125,182,187,206,213,273,278,300],"least":[122,184,209],"average":[124],"all":[127],"pairs,":[128],"also":[130],"give":[131],"alternative,":[133],"simpler":[134,227,253],"extract":[137,197],"single":[139],"pair.This":[141],"combinatorial":[142],"theorem":[143],"comes":[145],"handy":[146],"rounding":[148,169,331],"fractional":[150],"solution":[151],"LP":[154],"relaxation":[155],"maximum":[158,233,337,345],"Traveling":[159],"Salesman":[160],"Problem":[161],"(TSP)":[162],"problem.":[163],"The":[164],"first":[165],"stage":[166],"procedure":[170,332],"obtains":[171],"two":[172,265],"do":[176],"share":[178],"twice":[185,276],"optimal":[190],"solution.":[191],"Then":[192],"show":[194,287],"how":[195,288],"tour":[199,298],"from":[200,232,291],"2/3":[210],"longest":[216],"tour.":[217],"This":[218,311],"improves":[219,312],"upon":[220,313],"previous":[222,256,315],"5/8":[223],"approximation":[224,316,319,334],"algorithm.":[228],"Utilizing":[229],"reduction":[231],"TSP":[234,347],"shortest":[237],"superstring":[238],"problem,":[239,248],"obtain":[241,290],"2.5-approximation":[243],"for":[245,336],"latter":[247],"which":[249],"again":[251],"much":[252],"one.For":[257],"minimum":[258],"asymmetric":[259,346],"TSP,":[260],"same":[262],"technique":[263],"sharing":[269],"2-cycle,":[271],"optimum.":[281],"Assuming":[282],"triangle":[283,349],"inequality,":[284],"this":[292],"0.842":[304],"log":[305,323],"larger":[308],"optimal.":[310],"guarantee":[320],"0.999":[322],"Other":[327],"are":[333],"algorithms":[335],"3-cycle":[338],"cover":[339],"(factor":[340,351],"2/3,":[341],"previously":[342,353],"3/5)":[343],"inequality":[350],"10/13,":[352],"3/4).":[354]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":23},{"year":2012,"cited_by_count":11}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
