{"id":"https://openalex.org/W1985412388","doi":"https://doi.org/10.1137/06065934x","title":"Binary Space Partitions for Axis-Aligned Fat Rectangles","display_name":"Binary Space Partitions for Axis-Aligned Fat Rectangles","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1985412388","doi":"https://doi.org/10.1137/06065934x","mag":"1985412388"},"language":"en","primary_location":{"id":"doi:10.1137/06065934x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065934x","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/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":["toth@math.mit.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"toth@math.mit.edu#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030799674"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.6022,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87827184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"1","first_page":"429","last_page":"447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9944000244140625,"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":0.8839846849441528},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7656301259994507},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.727591335773468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6494878530502319},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6053056120872498},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5776691436767578},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49088746309280396},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.46528735756874084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36003297567367554},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27396082878112793},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13524144887924194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11600810289382935}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8839846849441528},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7656301259994507},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.727591335773468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494878530502319},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6053056120872498},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5776691436767578},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49088746309280396},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.46528735756874084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36003297567367554},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27396082878112793},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13524144887924194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11600810289382935},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06065934x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065934x","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"}],"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/W284308051","https://openalex.org/W1976012877","https://openalex.org/W1983698126","https://openalex.org/W1998402272","https://openalex.org/W2041492362","https://openalex.org/W2062612774","https://openalex.org/W2068297738","https://openalex.org/W2068416637","https://openalex.org/W2104872668","https://openalex.org/W2120039945","https://openalex.org/W2142728440","https://openalex.org/W2146448055","https://openalex.org/W2149634922","https://openalex.org/W2150580945","https://openalex.org/W2165041056","https://openalex.org/W2171708854","https://openalex.org/W2278560942","https://openalex.org/W2997709504","https://openalex.org/W4244064761"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W1971174658","https://openalex.org/W2734192830","https://openalex.org/W2099195351","https://openalex.org/W2015634066","https://openalex.org/W2069654053","https://openalex.org/W3046629113","https://openalex.org/W2048339306","https://openalex.org/W3127082728","https://openalex.org/W2067936666"],"abstract_inverted_index":{"It":[0],"is":[1,14],"shown":[2],"that":[3,71],"for":[4,57],"any":[5],"n":[6,63],"disjoint":[7,64],"axis-aligned":[8,65,74],"fat":[9,66],"rectangles":[10,67],"in":[11,33,68],"three-space":[12],"there":[13,61],"a":[15],"binary":[16],"space":[17],"partition":[18],"(BSP)":[19],"of":[20,42],"$O(n\\log^8":[21],"n)$":[22,26,36,78],"size":[23],"and":[24,28],"$O(\\log^5":[25],"height":[27],"it":[29],"can":[30],"be":[31],"constructed":[32],"$O(n":[34],"\\,\\mathrm{polylog}\\,":[35],"time.":[37],"This":[38],"improves":[39],"earlier":[40],"bounds":[41],"Agarwal":[43],"et":[44],"al.":[45],"[SIAM":[46],"J.":[47],"Comput.,":[48],"29":[49],"(2000),":[50],"pp.":[51],"1422\u20131448].":[52],"On":[53],"the":[54],"other":[55],"hand,":[56],"every":[58],"$n\\in":[59],"\\mathbb{N}$,":[60],"are":[62],"$\\mathbb{R}^3$":[69],"such":[70],"their":[72],"smallest":[73],"BSP":[75],"has":[76],"$\\Omega(n\\log":[77],"size.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
