{"id":"https://openalex.org/W1977333786","doi":"https://doi.org/10.1145/2582112.2582152","title":"Near-Linear Algorithms for Geometric Hitting Sets and Set Covers","display_name":"Near-Linear Algorithms for Geometric Hitting Sets and Set Covers","publication_year":2014,"publication_date":"2014-05-02","ids":{"openalex":"https://openalex.org/W1977333786","doi":"https://doi.org/10.1145/2582112.2582152","mag":"1977333786"},"language":"en","primary_location":{"id":"doi:10.1145/2582112.2582152","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","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/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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049738659","display_name":"Jiangwei Pan","orcid":"https://orcid.org/0000-0003-0397-8971"},"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":"Jiangwei Pan","raw_affiliation_strings":["Duke University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":13.9191,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.98755047,"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":"271","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9979000091552734,"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":0.9972000122070312,"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/set-cover-problem","display_name":"Set cover problem","score":0.7612252235412598},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6586814522743225},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5924695134162903},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5674834847450256},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5293066501617432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5235728621482849},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5145661234855652},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.5013730525970459},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.500187873840332},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3959497809410095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35388773679733276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29338985681533813}],"concepts":[{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.7612252235412598},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6586814522743225},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5924695134162903},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5674834847450256},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5293066501617432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5235728621482849},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5145661234855652},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.5013730525970459},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.500187873840332},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3959497809410095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35388773679733276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29338985681533813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2582112.2582152","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W596522316","https://openalex.org/W1507039213","https://openalex.org/W1537545978","https://openalex.org/W1547671143","https://openalex.org/W1560989141","https://openalex.org/W1581442026","https://openalex.org/W1964481538","https://openalex.org/W1964691748","https://openalex.org/W1968301997","https://openalex.org/W1975581100","https://openalex.org/W1987752344","https://openalex.org/W1988790447","https://openalex.org/W1993324779","https://openalex.org/W1995671037","https://openalex.org/W1999396007","https://openalex.org/W2006673860","https://openalex.org/W2011039300","https://openalex.org/W2013451793","https://openalex.org/W2018541722","https://openalex.org/W2022671649","https://openalex.org/W2025809050","https://openalex.org/W2048440529","https://openalex.org/W2053924317","https://openalex.org/W2054459484","https://openalex.org/W2059541050","https://openalex.org/W2060978628","https://openalex.org/W2071864516","https://openalex.org/W2103444054","https://openalex.org/W2103893986","https://openalex.org/W2106887613","https://openalex.org/W2119142868","https://openalex.org/W2122140789","https://openalex.org/W2124187705","https://openalex.org/W2126746199","https://openalex.org/W2127739958","https://openalex.org/W2134422938","https://openalex.org/W2135730283","https://openalex.org/W2136963423","https://openalex.org/W2138473336","https://openalex.org/W2140049544","https://openalex.org/W2143996311","https://openalex.org/W2148431844","https://openalex.org/W2149906774","https://openalex.org/W2150865801","https://openalex.org/W2153441719","https://openalex.org/W2159205115","https://openalex.org/W2163656645","https://openalex.org/W2186682076","https://openalex.org/W2295428206","https://openalex.org/W3145128584","https://openalex.org/W4206206918","https://openalex.org/W4235042979","https://openalex.org/W4246219036","https://openalex.org/W4251391716","https://openalex.org/W6811179486"],"related_works":["https://openalex.org/W2035485837","https://openalex.org/W2037870595","https://openalex.org/W2147086810","https://openalex.org/W3165916245","https://openalex.org/W2003676461","https://openalex.org/W4244934433","https://openalex.org/W4376639562","https://openalex.org/W1594413663","https://openalex.org/W1496354680","https://openalex.org/W1517616038"],"abstract_inverted_index":{"Given":[0],"a":[1,27,40,61,81,89,116,122],"finite":[2],"range":[3,93],"space":[4],"\u03a3":[5],"=":[6,11],"(X,":[7],"R),":[8],"with":[9,69],"N":[10],"|X|":[12],"+":[13],"|R|,":[14],"we":[15],"present":[16],"two":[17],"simple":[18],"algorithms,":[19,66],"based":[20],"on":[21],"the":[22,44,53],"multiplicative-weight":[23],"method,":[24],"for":[25,79,88,106],"computing":[26,80],"small-size":[28,82],"hitting":[29,83,108],"set":[30,32,84,86,109,111,117,123],"or":[31,85],"cover":[33,87,112],"of":[34,43,91,118,124],"\u03a3.":[35],"The":[36],"first":[37],"algorithm":[38,46,55],"is":[39,115],"simpler":[41],"variant":[42],"Br\u00f6nnimann-Goodrich":[45],"but":[47],"more":[48],"efficient":[49],"to":[50,76,99],"implement,":[51],"and":[52,110,120],"second":[54],"can":[56],"be":[57],"viewed":[58],"as":[59],"solving":[60],"two-player":[62],"zero-sum":[63],"game.":[64],"These":[65],"in":[67,126],"conjunction":[68],"some":[70],"standard":[71],"geometric":[72,92],"data":[73],"structures,":[74],"lead":[75,98],"near-linear":[77],"algorithms":[78,105],"number":[90],"spaces.":[94],"For":[95],"example,":[96],"they":[97],"O(N":[100],"polylog(N))":[101],"expected-time":[102],"randomized":[103],"O(1)-approximation":[104],"both":[107],"if":[113],"X":[114],"points":[119],"\u211c":[121],"disks":[125],"R2.":[127]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
