{"id":"https://openalex.org/W2047239272","doi":"https://doi.org/10.1145/2213977.2214014","title":"A near-linear time \u03b5-approximation algorithm for geometric bipartite matching","display_name":"A near-linear time \u03b5-approximation algorithm for geometric bipartite matching","publication_year":2012,"publication_date":"2012-05-19","ids":{"openalex":"https://openalex.org/W2047239272","doi":"https://doi.org/10.1145/2213977.2214014","mag":"2047239272"},"language":"en","primary_location":{"id":"doi:10.1145/2213977.2214014","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214014","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5008241289","display_name":"R. Sharathkumar","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Sharathkumar","raw_affiliation_strings":["Duke University, Durham, NC, USA"],"affiliations":[{"raw_affiliation_string":"Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058649592","display_name":"Pankaj K. Agarwal","orcid":"https://orcid.org/0000-0002-9439-181X"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["Duke University, Durham, NC, USA"],"affiliations":[{"raw_affiliation_string":"Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008241289"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":8.6011,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.97225849,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"385","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9970999956130981,"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/time-complexity","display_name":"Time complexity","score":0.6385769248008728},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6369017958641052},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6321970224380493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6242085099220276},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6131046414375305},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.5792319178581238},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5583234429359436},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5461814999580383},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5182459354400635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5028297305107117},{"id":"https://openalex.org/keywords/freivalds-algorithm","display_name":"Freivalds' algorithm","score":0.45981866121292114},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43999478220939636},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.43526381254196167},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4266066551208496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.366452693939209},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.20611408352851868},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1857454478740692},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.1511305570602417}],"concepts":[{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.6385769248008728},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6369017958641052},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6321970224380493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6242085099220276},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6131046414375305},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.5792319178581238},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5583234429359436},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5461814999580383},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5182459354400635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5028297305107117},{"id":"https://openalex.org/C38506071","wikidata":"https://www.wikidata.org/wiki/Q6522941","display_name":"Freivalds' algorithm","level":5,"score":0.45981866121292114},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43999478220939636},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.43526381254196167},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4266066551208496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.366452693939209},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.20611408352851868},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1857454478740692},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.1511305570602417},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2213977.2214014","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214014","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.406.7261","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.7261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/~pankaj/publications/papers/eps-match.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.1902","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.1902","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/~pankaj/publications/papers/eps-approx-match.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1868565867","https://openalex.org/W1969357318","https://openalex.org/W1991111385","https://openalex.org/W2003813631","https://openalex.org/W2007052372","https://openalex.org/W2027277859","https://openalex.org/W2037576616","https://openalex.org/W2044101024","https://openalex.org/W2053913299","https://openalex.org/W2065295938","https://openalex.org/W2069216960","https://openalex.org/W2070143657","https://openalex.org/W2091299439","https://openalex.org/W2100654743","https://openalex.org/W2110940003","https://openalex.org/W2138851467","https://openalex.org/W2145192475","https://openalex.org/W2157529519","https://openalex.org/W2165142526"],"related_works":["https://openalex.org/W2113270940","https://openalex.org/W2004283824","https://openalex.org/W2963158951","https://openalex.org/W2070751425","https://openalex.org/W4299980042","https://openalex.org/W1982530285","https://openalex.org/W2118860231","https://openalex.org/W2085573573","https://openalex.org/W1992104669","https://openalex.org/W2521054645"],"abstract_inverted_index":{"For":[0],"point":[1],"sets":[2],"A,B":[3],"\u2282":[4],"Rd,":[5],"|A|=|B|=n,":[6],"and":[7,32],"for":[8],"a":[9,50,56],"parameter":[10],"\u03b5":[11],">":[12],"0,":[13],"we":[14],"present":[15],"an":[16,26,64],"algorithm":[17,41,61,93,104],"that":[18,82,98],"computes,":[19],"in":[20,71],"O(n":[21,106],"poly(log":[22,107],"n,":[23],"1/\u03b5))":[24],"time,":[25],"\u03b5-approximate":[27],"perfect":[28],"matching":[29],"of":[30,77,86,102],"A":[31],"B":[33],"with":[34],"high":[35],"probability;":[36],"the":[37,47,75,78,83,87,92,99],"previously":[38],"best":[39],"known":[40],"takes":[42],"\u03a9(n3/2)":[43],"time.":[44],"We":[45,80],"approximate":[46,65],"Lp-norm":[48],"using":[49],"distance":[51],"function,":[52],"d(\u2022,\u2022)":[53,70],"based":[54],"on":[55],"randomly":[57],"shifted":[58],"quad-tree.":[59],"The":[60],"iteratively":[62],"generates":[63],"minimum-cost":[66],"augmenting":[67,88],"path":[68],"under":[69],"time":[72,101],"proportional":[73],"to":[74],"length":[76,85],"path.":[79],"show":[81],"total":[84],"paths":[89],"generated":[90],"by":[91],"is":[94,105],"O((n/\u03b5)log":[95],"n),":[96],"implying":[97],"running":[100],"our":[103],"n,1/\u03b5)).":[108]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}