{"id":"https://openalex.org/W3166722625","doi":"https://doi.org/10.1137/20m135950x","title":"A Shape Optimization Approach to the Problem of Covering a Two-Dimensional Region with Minimum-Radius Identical Balls","display_name":"A Shape Optimization Approach to the Problem of Covering a Two-Dimensional Region with Minimum-Radius Identical Balls","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3166722625","doi":"https://doi.org/10.1137/20m135950x","mag":"3166722625"},"language":"en","primary_location":{"id":"doi:10.1137/20m135950x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m135950x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.1137/20M135950X","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087290455","display_name":"Ernesto G. Birgin","orcid":"https://orcid.org/0000-0002-7466-7663"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. G. Birgin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7466-7663","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082364655","display_name":"Antoine Laurain","orcid":"https://orcid.org/0000-0002-8733-5190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Laurain","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8733-5190","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113947700","display_name":"Rafael Massambone","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Massambone","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043907764","display_name":"Arthur G. Santana","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. G. Santana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0822,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74449369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"43","issue":"3","first_page":"A2047","last_page":"A2078"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11115","display_name":"Topology Optimization in Engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.7692617177963257},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.715232253074646},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.6476023197174072},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6278990507125854},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.5087359547615051},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.498812198638916},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4839496910572052},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4467408061027527},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42508450150489807},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4226328730583191},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41145309805870056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33768904209136963},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27450329065322876},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10916298627853394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7692617177963257},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.715232253074646},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6476023197174072},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6278990507125854},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.5087359547615051},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.498812198638916},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4839496910572052},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4467408061027527},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42508450150489807},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4226328730583191},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41145309805870056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33768904209136963},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27450329065322876},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10916298627853394},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m135950x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m135950x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:003045207","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20M135950X","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:003045207","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20M135950X","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.46000000834465027,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G305158216","display_name":null,"funder_award_id":"2016/01860-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G4208676761","display_name":null,"funder_award_id":"2018/24293-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G4459137261","display_name":null,"funder_award_id":"408175/2018-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4684577688","display_name":null,"funder_award_id":"2019/25258-7","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5990746028","display_name":null,"funder_award_id":"2013/07375-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G7251383352","display_name":null,"funder_award_id":"304258/2018-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G865681276","display_name":null,"funder_award_id":"302682/2019-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1242194915","https://openalex.org/W1498180492","https://openalex.org/W1546275378","https://openalex.org/W1552637300","https://openalex.org/W1553719571","https://openalex.org/W1812401218","https://openalex.org/W1973734200","https://openalex.org/W1974425783","https://openalex.org/W1987995897","https://openalex.org/W2000320458","https://openalex.org/W2004041579","https://openalex.org/W2013201557","https://openalex.org/W2023341506","https://openalex.org/W2037091587","https://openalex.org/W2039539870","https://openalex.org/W2054895580","https://openalex.org/W2057624533","https://openalex.org/W2060988067","https://openalex.org/W2063958776","https://openalex.org/W2064582745","https://openalex.org/W2091542694","https://openalex.org/W2109255335","https://openalex.org/W2328722840","https://openalex.org/W2334357230","https://openalex.org/W2955809168","https://openalex.org/W2963067150","https://openalex.org/W2972854788","https://openalex.org/W2988894382","https://openalex.org/W3014094092","https://openalex.org/W3104103233"],"related_works":["https://openalex.org/W2576451984","https://openalex.org/W4253768562","https://openalex.org/W2151484740","https://openalex.org/W2702516025","https://openalex.org/W2228170291","https://openalex.org/W2080258733","https://openalex.org/W4298312405","https://openalex.org/W2950330786","https://openalex.org/W3092127437","https://openalex.org/W1970094780"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,9,12,40,43,46,53,61,65,69,77,83,100,113,116,119,144,149,152,164,169,189,197,205,221,232],"problem":[3,153,160,208],"of":[4,14,18,42,45,48,76,99,115,121,151,167,224],"covering":[5,227],"a":[6,157,181],"region":[7,22,54,170,190,198],"in":[8,35,82,148,203],"plane":[10],"with":[11,50,211,231],"union":[13,47],"$m$":[15],"identical":[16],"balls":[17,49],"minimum":[19],"radius.":[20],"The":[21,72,124,218],"to":[23,52,55,79,95,111,134,171,188],"be":[24,27,29,56,80,132,172,229],"covered":[25,57,173],"may":[26],"disconnected,":[28],"nonconvex,":[30],"have":[31,37],"Lipschitz":[32],"boundary,":[33],"and":[34,106,130,154],"particular":[36],"corners.":[38],"Nullifying":[39],"area":[41,78],"complement":[44],"respect":[51],"is":[58,68,85,127,161,174,199,209],"considered":[59,125],"as":[60],"constraint,":[62],"while":[63],"minimizing":[64],"balls'":[66],"radius":[67],"objective":[70],"function.":[71],"first-order":[73],"sensitivity":[74],"analysis":[75],"nullified":[81],"constraint":[84,117],"performed":[86],"using":[87],"shape":[88,102,122,139],"optimization":[89,140],"techniques.":[90],"Bi-Lipschitz":[91],"mappings":[92],"are":[93,216],"built":[94],"model":[96],"small":[97],"perturbations":[98],"nonsmooth":[101,138],"defined":[103],"via":[104,118],"unions":[105],"intersections;":[107],"this":[108],"allows":[109],"us":[110],"compute":[112],"derivative":[114],"notion":[120],"derivative.":[123],"approach":[126,215],"fairly":[128],"general":[129],"can":[131,228],"adapted":[133],"tackle":[135],"other":[136],"relevant":[137],"problems.":[141],"By":[142],"discretizing":[143],"integrals":[145],"that":[146],"appear":[147],"formulation":[150],"its":[155],"derivatives,":[156],"nonlinear":[158,206],"programming":[159,207],"obtained.":[162],"From":[163],"practical":[165],"point":[166],"view,":[168],"modeled":[175],"by":[176],"an":[177,212],"oracle":[178],"that,":[179],"for":[180],"given":[182],"point,":[183],"answers":[184],"whether":[185],"it":[186],"belongs":[187],"or":[191],"not.":[192],"No":[193],"additional":[194],"information":[195],"on":[196],"required.":[200],"Numerical":[201],"examples":[202],"which":[204],"solved":[210],"augmented":[213],"Lagrangian":[214],"presented.":[217],"experiments":[219],"illustrate":[220],"wide":[222],"variety":[223],"regions":[225],"whose":[226],"addressed":[230],"proposed":[233],"approach.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
