{"id":"https://openalex.org/W2591851020","doi":"https://doi.org/10.37236/6792","title":"On the Union Complexity of Families of Axis-Parallel Rectangles with a Low Packing Number","display_name":"On the Union Complexity of Families of Axis-Parallel Rectangles with a Low Packing Number","publication_year":2018,"publication_date":"2018-11-16","ids":{"openalex":"https://openalex.org/W2591851020","doi":"https://doi.org/10.37236/6792","mag":"2591851020"},"language":"en","primary_location":{"id":"doi:10.37236/6792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p32/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038150960","display_name":"Chaya Keller","orcid":"https://orcid.org/0000-0001-6400-3946"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Chaya Keller","raw_affiliation_strings":["Ben-Gurion University of the NEGEV"],"affiliations":[{"raw_affiliation_string":"Ben-Gurion University of the NEGEV","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071731808","display_name":"Shakhar Smorodinsky","orcid":"https://orcid.org/0000-0003-3038-6955"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shakhar Smorodinsky","raw_affiliation_strings":["Ben-Gurion University of the NEGEV"],"affiliations":[{"raw_affiliation_string":"Ben-Gurion University of the NEGEV","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038150960"],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00324948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.996999979019165,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9927999973297119,"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/combinatorics","display_name":"Combinatorics","score":0.8854682445526123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8299713730812073},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7571387887001038},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44068363308906555},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3323923349380493}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8854682445526123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8299713730812073},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7571387887001038},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44068363308906555},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3323923349380493},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/6792","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6792","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5276829180","display_name":null,"funder_award_id":"635/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7315415636","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2591851020.pdf","grobid_xml":"https://content.openalex.org/works/W2591851020.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1919151996","https://openalex.org/W2027190503","https://openalex.org/W2054236013","https://openalex.org/W2149757010","https://openalex.org/W2167816765","https://openalex.org/W4241794785","https://openalex.org/W4254977685","https://openalex.org/W4255489463","https://openalex.org/W6600024159","https://openalex.org/W6811179486","https://openalex.org/W6819423710"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Let":[0],"$\\mathcal{R}$":[1,35,46],"be":[2],"a":[3,25],"family":[4],"of":[5,18,34,45],"$n$":[6],"axis-parallel":[7],"rectangles":[8],"with":[9,24],"packing":[10],"number":[11],"$p-1$,":[12],"meaning":[13],"that":[14,30,41],"among":[15],"any":[16],"$p$":[17],"the":[19,31,42],"rectangles,":[20],"there":[21],"are":[22,55],"two":[23],"non-empty":[26],"intersection.":[27],"We":[28],"show":[29],"union":[32],"complexity":[33,44],"is":[36,47],"at":[37,48],"most":[38,49],"$O(n+p^2)$,":[39],"and":[40],"$(k-1)$-level":[43],"$O(n+k":[50],"p^2)$.":[51],"Both":[52],"upper":[53],"bounds":[54],"tight.":[56]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}