{"id":"https://openalex.org/W1969534344","doi":"https://doi.org/10.1137/s0097539700366103","title":"Edge-Disjoint Paths in Expander Graphs","display_name":"Edge-Disjoint Paths in Expander Graphs","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1969534344","doi":"https://doi.org/10.1137/s0097539700366103","mag":"1969534344"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539700366103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539700366103","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/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan M. Frieze","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.196,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.91052554,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"6","first_page":"1790","last_page":"1801"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8642643690109253},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7441831231117249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6920421123504639},{"id":"https://openalex.org/keywords/expander-graph","display_name":"Expander graph","score":0.5516079068183899},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5132839679718018},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5054035186767578},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47595497965812683},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45317959785461426},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44730162620544434},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42649561166763306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13154050707817078},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08643177151679993}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8642643690109253},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7441831231117249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6920421123504639},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.5516079068183899},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5132839679718018},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5054035186767578},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47595497965812683},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45317959785461426},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44730162620544434},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42649561166763306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13154050707817078},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08643177151679993},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539700366103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539700366103","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:10.1.1.19.5249","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.5249","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.aladdin.cs.cmu.edu/papers/pdfs/y2000/edp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.1924","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.1924","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/edp.ps.gz","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":14,"referenced_works":["https://openalex.org/W1971656597","https://openalex.org/W1980322272","https://openalex.org/W2001351653","https://openalex.org/W2005079828","https://openalex.org/W2032312374","https://openalex.org/W2046202598","https://openalex.org/W2058778915","https://openalex.org/W2059570262","https://openalex.org/W2072211488","https://openalex.org/W2081008200","https://openalex.org/W2139964991","https://openalex.org/W2610202827","https://openalex.org/W4235946010","https://openalex.org/W4255280903"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2078123803","https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W1491170033","https://openalex.org/W2734192830","https://openalex.org/W2099195351","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W2780684839"],"abstract_inverted_index":{"Given":[0],"a":[1,4,23,60,105],"graph":[2,73],"G=(V,E)and":[3],"set":[5,32],"of":[6,9,33,93,97],"$\\kappa$":[7,34,55],"pairs":[8,96],"vertices":[10,98],"in":[11,16,51,69],"V,":[12],"we":[13],"are":[14],"interested":[15],"finding,":[17],"for":[18,65],"each":[19],"pair":[20],"(ai,":[21],"bi),":[22],"path":[24],"connecting":[25],"ai":[26],"to":[27],"bi":[28],"such":[29],"that":[30,77],"the":[31,43],"paths":[35,68],"so":[36],"found":[37],"is":[38,45,50,56,87,103],"edge-disjoint.":[39],"For":[40],"arbitrary":[41],"graphs":[42],"problem":[44],"${\\cal":[46,52],"NP}$-complete,":[47],"although":[48],"it":[49],"P}$":[53],"if":[54,78],"fixed.":[57],"We":[58,75],"present":[59],"polynomial":[61],"time":[62],"randomized":[63],"algorithm":[64],"finding":[66],"edge-disjoint":[67],"an":[70],"r-regular":[71],"expander":[72],"G.":[74],"show":[76],"G":[79],"has":[80],"sufficiently":[81,88],"strong":[82],"expansion":[83],"properties":[84],"and":[85],"r":[86],"large,":[89],"then":[90],"all":[91],"sets":[92],"$\\kappa=\\Omega(n/\\log":[94],"n)$":[95],"can":[99],"be":[100],"joined.":[101],"This":[102],"within":[104],"constant":[106],"factorof":[107],"best":[108],"possible.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
