{"id":"https://openalex.org/W2170429689","doi":"https://doi.org/10.1007/s00454-007-9029-7","title":"Improved Bounds on the Union Complexity of Fat Objects","display_name":"Improved Bounds on the Union Complexity of Fat Objects","publication_year":2007,"publication_date":"2007-09-14","ids":{"openalex":"https://openalex.org/W2170429689","doi":"https://doi.org/10.1007/s00454-007-9029-7","mag":"2170429689"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-007-9029-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9029-7","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s00454-007-9029-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028410825","display_name":"Mark de Berg","orcid":"https://orcid.org/0000-0001-5770-3784"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Mark de Berg","raw_affiliation_strings":["Department of Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028410825"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":11.2669,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.98191601,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"40","issue":"1","first_page":"127","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9955999851226807,"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":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8269904851913452},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.734210729598999},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6358544230461121},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6183198094367981},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5608552098274231},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4890192449092865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3545186221599579},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1334238052368164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08997434377670288},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08205735683441162}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8269904851913452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.734210729598999},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6358544230461121},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6183198094367981},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5608552098274231},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4890192449092865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3545186221599579},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1334238052368164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08997434377670288},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08205735683441162},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-007-9029-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9029-7","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/65fe79c5-085d-48ff-8154-f4b4e3b2eb0b","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/65fe79c5-085d-48ff-8154-f4b4e3b2eb0b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Berg, de, M 2008, 'Improved bounds on the union complexity of fat objects', Discrete and Computational Geometry, vol. 40, no. 1, pp. 127-140. https://doi.org/10.1007/s00454-007-9029-7","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/65fe79c5-085d-48ff-8154-f4b4e3b2eb0b","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/65fe79c5-085d-48ff-8154-f4b4e3b2eb0b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 40(1), 127 - 140. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-007-9029-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9029-7","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1976173476","https://openalex.org/W1979838628","https://openalex.org/W1980092773","https://openalex.org/W2026200800","https://openalex.org/W2027190503","https://openalex.org/W2028747718","https://openalex.org/W2041935575","https://openalex.org/W2054236013","https://openalex.org/W2061495711","https://openalex.org/W2065106456","https://openalex.org/W2077120703","https://openalex.org/W2079010364","https://openalex.org/W2093778840","https://openalex.org/W2134898774","https://openalex.org/W2136863760","https://openalex.org/W2139161643","https://openalex.org/W2141110561","https://openalex.org/W2149906774","https://openalex.org/W2151942047","https://openalex.org/W2153204081","https://openalex.org/W2155923807","https://openalex.org/W2169945387","https://openalex.org/W2196955596","https://openalex.org/W2607182292","https://openalex.org/W4230857999","https://openalex.org/W4242246215","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W4288278856","https://openalex.org/W2572370460","https://openalex.org/W2949921337"],"abstract_inverted_index":{"We":[0,20],"introduce":[1],"a":[2,48],"new":[3],"class":[4,51],"of":[5,26,29,52],"fat,":[6],"not":[7],"necessarily":[8],"convex":[9],"or":[10],"polygonal,":[11],"objects":[12,32],"in":[13],"the":[14,23,40],"plane,":[15],"namely":[16],"locally":[17],"\u03b3-fat":[18],"objects.":[19,53],"prove":[21],"that":[22],"union":[24],"complexity":[25],"any":[27],"set":[28],"n":[30],"such":[31],"is":[33],"O(\u03bb":[34],"s+2(n)log":[35],"2":[36],"n).":[37],"This":[38],"improves":[39],"best":[41],"known":[42],"bound,":[43],"and":[44],"extends":[45],"it":[46],"to":[47],"more":[49],"general":[50]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}