{"id":"https://openalex.org/W2028363565","doi":"https://doi.org/10.1137/s0097539701395486","title":"Approximating the Longest Cycle Problem in Sparse Graphs","display_name":"Approximating the Longest Cycle Problem in Sparse Graphs","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2028363565","doi":"https://doi.org/10.1137/s0097539701395486","mag":"2028363565"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539701395486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539701395486","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/A5109192583","display_name":"Tom\u00e1s Feder","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tom\u00e1s Feder","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112649653","display_name":"Rajeev Motwani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajeev Motwani","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004849184","display_name":"Carlos Subi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Subi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109192583"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4489,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.89234754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"5","first_page":"1596","last_page":"1607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.861388087272644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6837099194526672},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.5832566618919373},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5238980054855347},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.5053642392158508},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4610058665275574},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4566440284252167},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.44901156425476074},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.42835530638694763},{"id":"https://openalex.org/keywords/pancyclic-graph","display_name":"Pancyclic graph","score":0.4254187345504761},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.32186079025268555},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.2880186438560486},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09407055377960205}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.861388087272644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6837099194526672},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.5832566618919373},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5238980054855347},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.5053642392158508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4610058665275574},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4566440284252167},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.44901156425476074},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.42835530638694763},{"id":"https://openalex.org/C166911692","wikidata":"https://www.wikidata.org/wiki/Q7130424","display_name":"Pancyclic graph","level":5,"score":0.4254187345504761},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.32186079025268555},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2880186438560486},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09407055377960205},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539701395486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539701395486","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:CiteSeerX.psu:10.1.1.110.1071","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.1071","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~tomas/cycle.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1586904125","https://openalex.org/W1967066104","https://openalex.org/W1976157781","https://openalex.org/W1994680554","https://openalex.org/W2005079828","https://openalex.org/W2019698871","https://openalex.org/W2023774253","https://openalex.org/W2027410688","https://openalex.org/W2066700938","https://openalex.org/W2074417667","https://openalex.org/W2084421815","https://openalex.org/W2327953950"],"related_works":["https://openalex.org/W4287117052","https://openalex.org/W2157783000","https://openalex.org/W3176308333","https://openalex.org/W203133463","https://openalex.org/W2019758609","https://openalex.org/W2969955840","https://openalex.org/W1979599997","https://openalex.org/W1864214016","https://openalex.org/W4300596390","https://openalex.org/W1428816444"],"abstract_inverted_index":{"We":[0,37,56,149,179],"consider":[1,39,150],"the":[2,40,151,174],"problem":[3,41],"of":[4,15,42,59,80,92,104,112,121,143,154,176,195,203,217],"finding":[5,43,77],"long":[6,44,177],"paths":[7],"and":[8,97,135,162,166,183],"cycles":[9,45,58,191,216],"in":[10,46,87],"Hamiltonian":[11,33,160],"graphs.":[12],"The":[13],"focus":[14],"our":[16],"work":[17],"is":[18,157],"on":[19,69],"sparse":[20],"graphs,":[21,24,34,165,188],"e.g.,":[22,35],"cubic":[23,48,164],"that":[25,117,156,181,192],"satisfy":[26],"some":[27],"property":[28,153],"known":[29],"to":[30,159,169,210],"hold":[31],"for":[32,65,76,107,185],"k-cyclability.":[36],"first":[38],"3-connected":[47,163,204],"graphs":[49,89,109,161,206],"whose":[50],"edges":[51],"have":[52,118],"weights":[53],"$w_i\\geq":[54],"0$.":[55],"find":[57,140,215],"weight":[60],"at":[61,82,94,114,132,145,219],"least":[62,83,146,220],"${(\\sum":[63],"w_i^a)}^{\\frac{1}{a}}$":[64],"$a=\\log_2":[66],"3$.":[67],"Based":[68],"this":[70,105],"result,":[71,106],"we":[72,139,167,199,213],"develop":[73],"an":[74],"algorithm":[75],"a":[78,102,119,127,141,201],"cycle":[79,120,142],"length":[81,122,144,218],"$m^{(\\log_3":[84],"2)/2}\\approx":[85],"m^{0.315}$":[86],"3-cyclable":[88,128],"with":[90,98,110,130,136,207],"vertices":[91,111],"degree":[93,113,187],"most":[95,115,133],"3":[96,116,134],"m":[99],"edges.":[100],"As":[101],"corollary":[103],"arbitrary":[108],"l":[123,137],"(or,":[124],"more":[125],"generally,":[126],"minor":[129],"degrees":[131,208],"edges),":[138],"$l^{(\\log_3":[147],"2)/2}$.":[148],"graph":[152],"1-toughness":[155,172],"common":[158],"try":[168],"determine":[170],"if":[171],"implies":[173],"existence":[175],"cycles.":[178],"show":[180],"2-connectivity":[182],"1-toughness,":[184],"constant":[186],"may":[189],"give":[190],"are":[193],"only":[194],"logarithmic":[196],"length.":[197],"However,":[198],"exhibit":[200],"class":[202],"1-tough":[205],"up":[209],"6,":[211],"where":[212],"can":[214],"${m}^{\\log_3":[221],"2}/2$.":[222]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
