{"id":"https://openalex.org/W2899517269","doi":"https://doi.org/10.1142/s0218195910003268","title":"OPTIMAL BSPs AND RECTILINEAR CARTOGRAMS","display_name":"OPTIMAL BSPs AND RECTILINEAR CARTOGRAMS","publication_year":2010,"publication_date":"2010-04-01","ids":{"openalex":"https://openalex.org/W2899517269","doi":"https://doi.org/10.1142/s0218195910003268","mag":"2899517269"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195910003268","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195910003268","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 & 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/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 Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065736235","display_name":"Elena Mumford","orcid":null},"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":false,"raw_author_name":"ELENA MUMFORD","raw_affiliation_strings":["Department of Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000420564","display_name":"Bettina Speckmann","orcid":"https://orcid.org/0000-0002-8514-7858"},"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":false,"raw_author_name":"BETTINA SPECKMANN","raw_affiliation_strings":["Department of Mathematics and Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and 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":3,"corresponding_author_ids":["https://openalex.org/A5028410825"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":6.5183,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.95825161,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"20","issue":"02","first_page":"203","last_page":"222"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9991000294685364,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.7610412836074829},{"id":"https://openalex.org/keywords/thematic-map","display_name":"Thematic map","score":0.7182973027229309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6177254915237427},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5662961006164551},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5400979518890381},{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.5244249105453491},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5141428112983704},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4977450668811798},{"id":"https://openalex.org/keywords/rectilinear-polygon","display_name":"Rectilinear polygon","score":0.4905363917350769},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.48755544424057007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4499828815460205},{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.43816742300987244},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.437010794878006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.270250141620636},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.18469300866127014},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13653582334518433},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.12902316451072693},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.11730465292930603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08644217252731323},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.07780659198760986}],"concepts":[{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.7610412836074829},{"id":"https://openalex.org/C93692415","wikidata":"https://www.wikidata.org/wiki/Q1502030","display_name":"Thematic map","level":2,"score":0.7182973027229309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6177254915237427},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5662961006164551},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5400979518890381},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.5244249105453491},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5141428112983704},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4977450668811798},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.4905363917350769},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.48755544424057007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4499828815460205},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.43816742300987244},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.437010794878006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.270250141620636},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.18469300866127014},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13653582334518433},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.12902316451072693},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.11730465292930603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08644217252731323},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.07780659198760986},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218195910003268","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195910003268","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 & Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/1a78db69-9994-43a1-a4ab-9e4087e61269","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/1a78db69-9994-43a1-a4ab-9e4087e61269","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, Mumford, E & Speckmann, B 2010, 'Optimal BSPs and rectilinear cartograms', International Journal of Computational Geometry and Applications, vol. 20, no. 2, pp. 203-222. https://doi.org/10.1142/S0218195910003268","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/1a78db69-9994-43a1-a4ab-9e4087e61269","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/1a78db69-9994-43a1-a4ab-9e4087e61269","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":"International Journal of Computational Geometry and Applications, 20(2), 203 - 222. World Scientific","raw_type":"info:eu-repo/semantics/article"}],"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/W102566572","https://openalex.org/W1507189098","https://openalex.org/W1585686737","https://openalex.org/W1964716955","https://openalex.org/W1994432275","https://openalex.org/W2003147772","https://openalex.org/W2071807189","https://openalex.org/W2074429597","https://openalex.org/W2105795805","https://openalex.org/W2130716604","https://openalex.org/W2133185801","https://openalex.org/W2138620696","https://openalex.org/W2148734466","https://openalex.org/W2148987114","https://openalex.org/W2151045902","https://openalex.org/W2199159668","https://openalex.org/W2322867406","https://openalex.org/W3145128584","https://openalex.org/W4241761266","https://openalex.org/W4246219036"],"related_works":["https://openalex.org/W2466150543","https://openalex.org/W2368761166","https://openalex.org/W1848854318","https://openalex.org/W2383351568","https://openalex.org/W4295111764","https://openalex.org/W2362048241","https://openalex.org/W2383234567","https://openalex.org/W100228941","https://openalex.org/W2097069316","https://openalex.org/W1532062818"],"abstract_inverted_index":{"A":[0],"cartogram":[1,27],"is":[2,47,100],"a":[3,11,23,26,30,50,96,107,124,147],"thematic":[4],"map":[5],"that":[6,99],"visualizes":[7],"statistical":[8],"data":[9,68],"about":[10],"set":[12],"of":[13,22,73,127,158],"regions":[14,72,79],"like":[15],"countries,":[16],"states":[17],"or":[18],"provinces.":[19],"The":[20],"size":[21,131],"region":[24,46,59],"in":[25,102,138],"corresponds":[28],"to":[29,141,152,155],"particular":[31],"geographic":[32],"variable,":[33],"for":[34,41,90,110,117,123],"example,":[35],"population.":[36],"We":[37,134],"present":[38],"an":[39],"algorithm":[40,65,94,109,121],"constructing":[42,157],"rectilinear":[43,51,118],"cartograms":[44],"(each":[45],"represented":[48],"by":[49],"polygon)":[52],"with":[53],"zero":[54],"cartographic":[55],"error":[56],"and":[57,61,87,132],"correct":[58,88],"adjacencies,":[60],"we":[62,145],"test":[63],"our":[64,139],"on":[66],"various":[67],"sets.":[69],"It":[70],"produces":[71],"very":[74],"small":[75],"complexity\u2014in":[76],"fact,":[77],"most":[78],"are":[80],"rectangles\u2014while":[81],"still":[82],"ensuring":[83],"both":[84],"exact":[85],"areas":[86],"adjacencies":[89],"all":[91],"regions.":[92],"Our":[93],"uses":[95],"novel":[97],"subroutine":[98],"interesting":[101],"its":[103],"own":[104],"right,":[105],"namely":[106],"polynomial-time":[108],"computing":[111,142],"optimal":[112],"binary":[113],"space":[114],"partitions":[115],"(BSPs)":[116],"maps.":[119],"This":[120],"works":[122],"general":[125],"class":[126],"optimality":[128],"criteria,":[129],"including":[130],"depth.":[133],"use":[135],"this":[136],"generality":[137],"application":[140],"cartograms,":[143],"where":[144],"apply":[146],"dedicated":[148],"cost":[149],"function":[150],"leading":[151],"BSPs":[153],"amenable":[154],"the":[156],"high-quality":[159],"cartograms.":[160]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}