{"id":"https://openalex.org/W2003356218","doi":"https://doi.org/10.1145/2261250.2261267","title":"On Klee's measure problem for grounded boxes","display_name":"On Klee's measure problem for grounded boxes","publication_year":2012,"publication_date":"2012-06-17","ids":{"openalex":"https://openalex.org/W2003356218","doi":"https://doi.org/10.1145/2261250.2261267","mag":"2003356218"},"language":"en","primary_location":{"id":"doi:10.1145/2261250.2261267","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2261250.2261267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-eighth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100764686","display_name":"Hakan Y\u0131ld\u0131z","orcid":"https://orcid.org/0000-0002-9579-4338"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hakan Yildiz","raw_affiliation_strings":["University of California, Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072397842","display_name":"Subhash Suri","orcid":"https://orcid.org/0000-0002-5668-7521"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subhash Suri","raw_affiliation_strings":["University of California, Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":8.5463,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.98628963,"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":"111","last_page":"120"},"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":0.9965000152587891,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/measure","display_name":"Measure (data warehouse)","score":0.7419357299804688},{"id":"https://openalex.org/keywords/grounded-theory","display_name":"Grounded theory","score":0.6058987975120544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5719395875930786},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3235057592391968},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.16483786702156067},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.13402754068374634},{"id":"https://openalex.org/keywords/qualitative-research","display_name":"Qualitative research","score":0.10740894079208374},{"id":"https://openalex.org/keywords/social-science","display_name":"Social science","score":0.05020168423652649}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7419357299804688},{"id":"https://openalex.org/C156325361","wikidata":"https://www.wikidata.org/wiki/Q1152864","display_name":"Grounded theory","level":3,"score":0.6058987975120544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5719395875930786},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3235057592391968},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.16483786702156067},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.13402754068374634},{"id":"https://openalex.org/C190248442","wikidata":"https://www.wikidata.org/wiki/Q839486","display_name":"Qualitative research","level":2,"score":0.10740894079208374},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.05020168423652649}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2261250.2261267","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2261250.2261267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-eighth annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.9741","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.9741","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ucsb.edu/~suri/psdir/socg12.pdf","raw_type":"text"},{"id":"pmh:oai:https://open.metu.edu.tr:11511/93565","is_oa":false,"landing_page_url":"https://hdl.handle.net/11511/93565","pdf_url":null,"source":{"id":"https://openalex.org/S4306402495","display_name":"OpenMETU (Middle East Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201799495","host_organization_name":"Middle East Technical University","host_organization_lineage":["https://openalex.org/I201799495"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"28th Annual Symposuim on Computational Geometry, SCG 2012","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W47700306","https://openalex.org/W1588375755","https://openalex.org/W1998505959","https://openalex.org/W2015690843","https://openalex.org/W2019725409","https://openalex.org/W2022093184","https://openalex.org/W2034834234","https://openalex.org/W2046074631","https://openalex.org/W2079176421","https://openalex.org/W2100830227","https://openalex.org/W2101672259","https://openalex.org/W2129392074","https://openalex.org/W2138075238","https://openalex.org/W2149906774","https://openalex.org/W2151953637","https://openalex.org/W2327699610","https://openalex.org/W2463564488","https://openalex.org/W2513470175","https://openalex.org/W2970974516","https://openalex.org/W3122481131"],"related_works":["https://openalex.org/W2422371469","https://openalex.org/W4240046694","https://openalex.org/W4214924096","https://openalex.org/W4246418678","https://openalex.org/W2135024282","https://openalex.org/W4235112656","https://openalex.org/W2643419842","https://openalex.org/W2385729804","https://openalex.org/W2361017481","https://openalex.org/W2318371068"],"abstract_inverted_index":{"A":[0],"well-known":[1],"problem":[2,30,158,164,171,176],"in":[3,21,66,123,165],"computational":[4],"geometry":[5],"is":[6,63,79,96,153],"Klee's":[7,28,86],"measure":[8,29,87],"problem,":[9,134],"which":[10,184],"asks":[11],"for":[12,31,84,88,114,117],"the":[13,32,42,104,108,124,131,135,156,179],"volume":[14,163,170],"of":[15,18,40,53,61,91,99,107,127,150,177,181,187],"a":[16,36,45,51,59,67,73,89,143,160,174],"union":[17],"axis-aligned":[19],"boxes":[20,43,54,62],"d-space.":[22],"In":[23],"this":[24],"paper,":[25],"we":[26],"consider":[27],"special":[33,125],"case":[34,126],"where":[35],"2-dimensional":[37],"orthogonal":[38,69],"projection":[39,70],"all":[41],"has":[44],"common":[46,74],"corner.":[47,75],"We":[48],"call":[49],"such":[50],"set":[52,60,90],"2-grounded":[55,93],"and,":[56],"more":[57],"generally,":[58],"k-grounded":[64,115],"if":[65],"k-dimensional":[68],"they":[71],"share":[72],"Our":[76],"main":[77],"result":[78],"an":[80,97],"O(n(d-1)/2log2n)":[81],"time":[82,136],"algorithm":[83,112],"computing":[85],"n":[92,145],"boxes.":[94],"This":[95],"improvement":[98],"roughly":[100],"O(\u221an)":[101],"compared":[102],"to":[103,154,159],"fastest":[105],"solution":[106],"general":[109],"problem.":[110],"The":[111,147,168],"works":[113],"boxes,":[116],"any":[118],"k":[119],"\u2265":[120],"2,":[121],"and":[122],"k=d,":[128],"also":[129],"called":[130],"hypervolume":[132],"indicator":[133],"bound":[137],"can":[138],"be":[139,186],"improved":[140],"further":[141],"by":[142],"log":[144],"factor.":[146],"key":[148],"idea":[149],"our":[151],"technique":[152],"reduce":[155],"d-dimensional":[157],"semi-dynamic":[161],"weighted":[162,169],"dimension":[166],"d-2.":[167],"requires":[172],"solving":[173],"combinatorial":[175],"maintaining":[178],"sum":[180],"ordered":[182],"products,":[183],"may":[185],"independent":[188],"interest.":[189]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"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":4},{"year":2013,"cited_by_count":12}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
