{"id":"https://openalex.org/W2035332367","doi":"https://doi.org/10.1109/cec.2009.4983115","title":"Towards an evolved lower bound for the most circular partition of a square","display_name":"Towards an evolved lower bound for the most circular partition of a square","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2035332367","doi":"https://doi.org/10.1109/cec.2009.4983115","mag":"2035332367"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2009.4983115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-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/A5013030547","display_name":"Claudia Obermaier","orcid":null},"institutions":[{"id":"https://openalex.org/I2802076133","display_name":"University of Koblenz and Landau","ror":"https://ror.org/01j9f6752","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802076133"]},{"id":"https://openalex.org/I4387153937","display_name":"Universit\u00e4t Koblenz","ror":"https://ror.org/0433e6t24","country_code":null,"type":"education","lineage":["https://openalex.org/I4387153937"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Claudia Obermaier","raw_affiliation_strings":["Artificial Intelligence Research Group, University of Koblenz and Landau, Koblenz, Germany","Artificial Intelligence Research Group, University of Koblenz-Landau, 56016, Germany"],"affiliations":[{"raw_affiliation_string":"Artificial Intelligence Research Group, University of Koblenz and Landau, Koblenz, Germany","institution_ids":["https://openalex.org/I2802076133"]},{"raw_affiliation_string":"Artificial Intelligence Research Group, University of Koblenz-Landau, 56016, Germany","institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056886268","display_name":"Markus Wagner","orcid":"https://orcid.org/0000-0002-3124-0061"},"institutions":[{"id":"https://openalex.org/I4387153937","display_name":"Universit\u00e4t Koblenz","ror":"https://ror.org/0433e6t24","country_code":null,"type":"education","lineage":["https://openalex.org/I4387153937"]},{"id":"https://openalex.org/I2802076133","display_name":"University of Koblenz and Landau","ror":"https://ror.org/01j9f6752","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802076133"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Wagner","raw_affiliation_strings":["Artificial Intelligence Research Group, University of Koblenz and Landau, Koblenz, Germany","Artificial Intelligence Research Group, University of Koblenz-Landau, 56016, Germany"],"affiliations":[{"raw_affiliation_string":"Artificial Intelligence Research Group, University of Koblenz and Landau, Koblenz, Germany","institution_ids":["https://openalex.org/I2802076133"]},{"raw_affiliation_string":"Artificial Intelligence Research Group, University of Koblenz-Landau, 56016, Germany","institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013030547"],"corresponding_institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10694582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":null,"first_page":"1463","last_page":"1469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9945999979972839,"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/T12504","display_name":"Mathematics and Applications","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/equilateral-triangle","display_name":"Equilateral triangle","score":0.8187773823738098},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.7638225555419922},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7130013108253479},{"id":"https://openalex.org/keywords/inscribed-figure","display_name":"Inscribed figure","score":0.7091682553291321},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.7006524205207825},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6974636316299438},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.6583216190338135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6226693391799927},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.49009501934051514},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.4885052442550659},{"id":"https://openalex.org/keywords/aspect-ratio","display_name":"Aspect ratio (aeronautics)","score":0.4774758815765381},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4307795763015747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32805582880973816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23689568042755127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11075994372367859},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10351872444152832}],"concepts":[{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.8187773823738098},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7638225555419922},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7130013108253479},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.7091682553291321},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7006524205207825},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6974636316299438},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6583216190338135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6226693391799927},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.49009501934051514},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.4885052442550659},{"id":"https://openalex.org/C82558694","wikidata":"https://www.wikidata.org/wiki/Q1545619","display_name":"Aspect ratio (aeronautics)","level":2,"score":0.4774758815765381},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4307795763015747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32805582880973816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23689568042755127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11075994372367859},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10351872444152832},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cec.2009.4983115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.725.3469","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.725.3469","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cs.adelaide.edu.au/%7Emarkus/pub/2009cec.pdf","raw_type":"text"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/76748","is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/76748","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1109/cec.2009.4983115","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W79131202","https://openalex.org/W1490482062","https://openalex.org/W1497256448","https://openalex.org/W1603006021","https://openalex.org/W1609997951","https://openalex.org/W1639032689","https://openalex.org/W1978970913","https://openalex.org/W2027037071","https://openalex.org/W2046631983","https://openalex.org/W2058909271","https://openalex.org/W2069229314","https://openalex.org/W2079010364","https://openalex.org/W2087027878","https://openalex.org/W2124607527","https://openalex.org/W2132031653","https://openalex.org/W2168897714","https://openalex.org/W2278480541","https://openalex.org/W2284330674","https://openalex.org/W2307045567","https://openalex.org/W2486609979","https://openalex.org/W2496050832","https://openalex.org/W3023540311","https://openalex.org/W3023768696","https://openalex.org/W6635972241","https://openalex.org/W6661965361","https://openalex.org/W6678223940","https://openalex.org/W6698275089"],"related_works":["https://openalex.org/W2969699582","https://openalex.org/W3128759501","https://openalex.org/W1938473727","https://openalex.org/W2205924205","https://openalex.org/W2043979935","https://openalex.org/W2165083794","https://openalex.org/W4287184648","https://openalex.org/W2153732620","https://openalex.org/W2145651789","https://openalex.org/W3165507086"],"abstract_inverted_index":{"We":[0,86],"examine":[1],"the":[2,20,38,41,44,49,59,73,78,98],"problem":[3,54],"of":[4,33,40,43,75,100],"partitioning":[5],"a":[6,34,76,91],"square":[7],"into":[8],"convex":[9,35],"polygons":[10],"which":[11,93],"are":[12,87],"as":[13,15,62,64],"circular":[14],"possible.":[16],"Circular":[17],"means":[18],"that":[19],"polygon's":[21],"aspect":[22,31],"ratio":[23,39],"is":[24,81,94],"supposed":[25],"to":[26,48,89],"be":[27],"near":[28],"1.":[29],"The":[30],"ration":[32],"polygon":[36],"denotes":[37],"diameters":[42],"smallest":[45],"circumscribing":[46],"circle":[47],"largest":[50],"inscribed":[51],"disk.":[52],"This":[53],"has":[55],"been":[56],"solved":[57],"for":[58,65],"equilateral":[60],"triangle":[61],"well":[63],"regular":[66],"k-gon":[67],"with":[68,97],"k":[69],">":[70],"4.":[71],"In":[72],"case":[74],"square,":[77],"optimal":[79],"solution":[80,92],"still":[82],"an":[83],"open":[84],"problem.":[85],"planning":[88],"find":[90],"ldquogood":[95],"enoughrdquo":[96],"help":[99],"evolutionary":[101],"algorithms.":[102]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
