{"id":"https://openalex.org/W2112104566","doi":"https://doi.org/10.1142/s0218195905001865","title":"SEPARATING POINTS BY AXIS-PARALLEL LINES","display_name":"SEPARATING POINTS BY AXIS-PARALLEL LINES","publication_year":2005,"publication_date":"2005-12-01","ids":{"openalex":"https://openalex.org/W2112104566","doi":"https://doi.org/10.1142/s0218195905001865","mag":"2112104566"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195905001865","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195905001865","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","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/A5030046558","display_name":"Grui\u0103 C\u00e4linescu","orcid":"https://orcid.org/0000-0002-0925-9524"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"GRUIA C\u0102LINESCU","raw_affiliation_strings":["Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091313409","display_name":"Adrian Dumitrescu","orcid":"https://orcid.org/0000-0002-1118-0321"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ADRIAN DUMITRESCU","raw_affiliation_strings":["Computer Science, University of Wisconsin\u2013Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53211, USA","Computer Science, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53211, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, University of Wisconsin\u2013Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53211, USA","institution_ids":["https://openalex.org/I43579087"]},{"raw_affiliation_string":"Computer Science, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53211, USA","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087578885","display_name":"Howard Karloff","orcid":"https://orcid.org/0000-0003-4490-2324"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"HOWARD KARLOFF","raw_affiliation_strings":["AT&amp;T Labs\u2013Research, 180 Park Ave., Florham Park, NJ 07932, USA","AT&T Labs - Research, 180 Park Ave, Florham Park, NJ 07932, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AT&amp;T Labs\u2013Research, 180 Park Ave., Florham Park, NJ 07932, USA","institution_ids":["https://openalex.org/I1283103587"]},{"raw_affiliation_string":"AT&T Labs - Research, 180 Park Ave, Florham Park, NJ 07932, USA#TAB#","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036031118","display_name":"Peng\u2010Jun Wan","orcid":"https://orcid.org/0000-0001-7926-5711"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"PENG-JUN WAN","raw_affiliation_strings":["Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7512,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.79171986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"06","first_page":"575","last_page":"590"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12176","display_name":"Optimization and Packing Problems","score":0.9966999888420105,"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/rounding","display_name":"Rounding","score":0.8723970651626587},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.8186308145523071},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7509909868240356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7105706334114075},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6544399857521057},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6477649211883545},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5106428265571594},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.46874290704727173},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33687347173690796},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19433912634849548},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1593811810016632}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.8723970651626587},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.8186308145523071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7509909868240356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7105706334114075},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6544399857521057},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6477649211883545},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5106428265571594},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.46874290704727173},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33687347173690796},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19433912634849548},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1593811810016632},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195905001865","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195905001865","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W976710","https://openalex.org/W37461142","https://openalex.org/W1994612875","https://openalex.org/W2011039300","https://openalex.org/W2103772568","https://openalex.org/W2112823227","https://openalex.org/W2142766864","https://openalex.org/W2148901826","https://openalex.org/W2476096155","https://openalex.org/W2611804663","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W4220780102","https://openalex.org/W1502401885","https://openalex.org/W2410881844","https://openalex.org/W3196334750","https://openalex.org/W2004257129","https://openalex.org/W2097569240","https://openalex.org/W2543175834","https://openalex.org/W2468848027","https://openalex.org/W1527755298"],"abstract_inverted_index":{"We":[0,66,117,131],"study":[1],"the":[2,9,16,31,38,79,84,98,103,127,134,138],"problem":[3,58,101,106],"of":[4,13,25,37,62,137],"separating":[5],"n":[6],"points":[7,85],"in":[8,82],"plane,":[10],"no":[11],"two":[12],"which":[14,83,123],"have":[15],"same":[17],"x-":[18],"or":[19],"y-coordinate,":[20],"using":[21,90],"a":[22,68,75],"minimum":[23],"number":[24],"vertical":[26],"and":[27,59,74],"horizontal":[28],"lines":[29],"avoiding":[30],"points,":[32],"so":[33],"that":[34,56,133],"each":[35],"cell":[36],"subdivision":[39],"contains":[40],"at":[41],"most":[42],"one":[43],"point.":[44],"Extending":[45],"previous":[46],"NP-hardness":[47],"results":[48],"due":[49],"to":[50,87,102],"Freimer":[51],"et":[52,110],"al.":[53,111],"we":[54,96],"prove":[55],"this":[57,72,94],"some":[60],"variants":[61],"it":[63],"are":[64,86],"APX-hard.":[65],"give":[67],"2-approximation":[69],"algorithm":[70,77,114],"for":[71,78,126],"problem,":[73],"d-approximation":[76],"d-dimensional":[80],"variant,":[81],"be":[88],"separated":[89],"axis-parallel":[91],"hyperplanes.":[92],"To":[93],"end,":[95],"reduce":[97],"point":[99],"separation":[100],"rectangle":[104,128],"stabbing":[105,129],"studied":[107],"by":[108],"Gaur":[109],"Their":[112],"approximation":[113],"uses":[115],"LP-rounding.":[116],"present":[118],"an":[119],"alternative":[120],"LP-rounding":[121],"procedure":[122],"also":[124],"works":[125],"problem.":[130],"show":[132],"integrality":[135],"ratio":[136],"LP":[139],"is":[140],"exactly":[141],"2.":[142]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
