{"id":"https://openalex.org/W2950870475","doi":"https://doi.org/10.1007/s00454-022-00422-8","title":"Packing Disks into Disks with Optimal Worst-Case Density","display_name":"Packing Disks into Disks with Optimal Worst-Case Density","publication_year":2022,"publication_date":"2022-09-15","ids":{"openalex":"https://openalex.org/W2950870475","doi":"https://doi.org/10.1007/s00454-022-00422-8","mag":"2950870475"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-022-00422-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-022-00422-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-022-00422-8.pdf","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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-022-00422-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015542807","display_name":"S\u00e1ndor P. Fekete","orcid":"https://orcid.org/0000-0002-9062-4241"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"S\u00e1ndor P. Fekete","raw_affiliation_strings":["Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9062-4241","affiliations":[{"raw_affiliation_string":"Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076288432","display_name":"Phillip Keldenich","orcid":"https://orcid.org/0000-0002-6677-5090"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Phillip Keldenich","raw_affiliation_strings":["Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080464077","display_name":"Christian Scheffer","orcid":"https://orcid.org/0000-0002-3471-2706"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Scheffer","raw_affiliation_strings":["Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms Group, Department of Computer Science, Braunschweig University of Technology, M\u00fchlenpfordtstr. 23, 38106, Brunswick, Germany","institution_ids":["https://openalex.org/I94509681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015542807"],"corresponding_institution_ids":["https://openalex.org/I94509681"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.9008,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75331323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"69","issue":"1","first_page":"51","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980999827384949,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.6780134439468384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47615596652030945}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6780134439468384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47615596652030945}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-022-00422-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-022-00422-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-022-00422-8.pdf","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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-022-00422-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-022-00422-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-022-00422-8.pdf","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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5662025764","display_name":null,"funder_award_id":"FE407/17-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950870475.pdf","grobid_xml":"https://content.openalex.org/works/W2950870475.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W239990970","https://openalex.org/W349093217","https://openalex.org/W1549020821","https://openalex.org/W1941056891","https://openalex.org/W1979411905","https://openalex.org/W1985317896","https://openalex.org/W2029049650","https://openalex.org/W2039006199","https://openalex.org/W2044646886","https://openalex.org/W2055789678","https://openalex.org/W2078608781","https://openalex.org/W2081874143","https://openalex.org/W2090164772","https://openalex.org/W2094475624","https://openalex.org/W2097665137","https://openalex.org/W2140512904","https://openalex.org/W2209399941","https://openalex.org/W2314767381","https://openalex.org/W2315522554","https://openalex.org/W2318644615","https://openalex.org/W2331302099","https://openalex.org/W2568571446","https://openalex.org/W2915128166","https://openalex.org/W3135993307","https://openalex.org/W4251859436"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"provide":[2],"a":[3,7,15,25,60,107,113,134],"tight":[4],"result":[5,129],"for":[6,69,137],"fundamental":[8],"problem":[9],"arising":[10],"from":[11],"packing":[12,22,142],"disks":[13,23,38,85],"into":[14,59],"circular":[16],"container:":[17],"The":[18,104],"critical":[19],"density":[20],"of":[21,34,39,62,84,86,140],"in":[24],"disk":[26,61],"is":[27,118,130],"0.5.":[28],"This":[29],"implies":[30],"that":[31,100,117],"any":[32,70],"set":[33],"(not":[35],"necessarily":[36],"equal)":[37],"total":[40],"area":[41,63,87],"$$\\delta":[42],"\\le":[43],"1/2$$":[44],"<mml:math":[45,73,90],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[46,74,91],"<mml:mrow>":[47,75,92],"<mml:mi>\u03b4</mml:mi>":[48],"<mml:mo>\u2264</mml:mo>":[49],"<mml:mn>1</mml:mn>":[50,93],"<mml:mo>/</mml:mo>":[51,94],"<mml:mn>2</mml:mn>":[52,95],"</mml:mrow>":[53,79,98],"</mml:math>":[54,80,99],"can":[55],"always":[56],"be":[57,102],"packed":[58],"1;":[64],"on":[65,120],"the":[66,124,138],"other":[67],"hand,":[68],"$$\\varepsilon":[71],"&gt;0$$":[72],"<mml:mi>\u03b5</mml:mi>":[76,97],"<mml:mo>&gt;</mml:mo>":[77],"<mml:mn>0</mml:mn>":[78],"there":[81],"are":[82],"sets":[83],"$$1/2+\\varepsilon":[88],"$$":[89],"<mml:mo>+</mml:mo>":[96],"cannot":[101],"packed.":[103],"proof":[105],"uses":[106],"careful":[108],"manual":[109],"analysis,":[110],"complemented":[111],"by":[112],"minor":[114],"automatic":[115],"part":[116],"based":[119],"interval":[121],"arithmetic.":[122],"Beyond":[123],"basic":[125],"mathematical":[126],"importance,":[127],"our":[128],"also":[131],"useful":[132],"as":[133],"blackbox":[135],"lemma":[136],"analysis":[139],"recursive":[141],"algorithms.":[143]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}