{"id":"https://openalex.org/W4414051275","doi":"https://doi.org/10.1007/s00454-025-00768-9","title":"The Geodesic Edge Center of a Simple Polygon","display_name":"The Geodesic Edge Center of a Simple Polygon","publication_year":2025,"publication_date":"2025-09-08","ids":{"openalex":"https://openalex.org/W4414051275","doi":"https://doi.org/10.1007/s00454-025-00768-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-025-00768-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00768-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00768-9.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/s00454-025-00768-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044299176","display_name":"Anna Lubiw","orcid":"https://orcid.org/0000-0002-2338-361X"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Anna Lubiw","raw_affiliation_strings":["David R.\u00a0Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"David R.\u00a0Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055963596","display_name":"Anurag Murty Naredla","orcid":"https://orcid.org/0000-0002-3577-903X"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","DE"],"is_corresponding":false,"raw_author_name":"Anurag Murty Naredla","raw_affiliation_strings":["David R.\u00a0Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada","Institut f\u00fcr Informatik, University of Bonn, Bonn, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3577-903X","affiliations":[{"raw_affiliation_string":"David R.\u00a0Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik, University of Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044299176"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.40495751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"74","issue":"4","first_page":"944","last_page":"998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9930999875068665,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9861999750137329,"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/geodesic","display_name":"Geodesic","score":0.8898000121116638},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8673999905586243},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.8453999757766724},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.6118000149726868},{"id":"https://openalex.org/keywords/weighted-voronoi-diagram","display_name":"Weighted Voronoi diagram","score":0.5949000120162964},{"id":"https://openalex.org/keywords/geodesic-map","display_name":"Geodesic map","score":0.5160999894142151},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.5030999779701233},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.5027999877929688}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8898000121116638},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8673999905586243},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.8453999757766724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6769999861717224},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6118000149726868},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.5949000120162964},{"id":"https://openalex.org/C162269530","wikidata":"https://www.wikidata.org/wiki/Q17100560","display_name":"Geodesic map","level":3,"score":0.5160999894142151},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.5030999779701233},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.5027999877929688},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.4472000002861023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4440000057220459},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.3612000048160553},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3528999984264374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.33550000190734863},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.3248000144958496},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.259799987077713}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00768-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00768-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00768-9.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/s00454-025-00768-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00768-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00768-9.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":[],"funders":[{"id":"https://openalex.org/F4320324900","display_name":"Rheinische Friedrich-Wilhelms-Universit\u00e4t Bonn","ror":"https://ror.org/041nas322"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414051275.pdf","grobid_xml":"https://content.openalex.org/works/W4414051275.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W183253369","https://openalex.org/W596522316","https://openalex.org/W1610448541","https://openalex.org/W1862650283","https://openalex.org/W1968134246","https://openalex.org/W1975883249","https://openalex.org/W2005411543","https://openalex.org/W2007610503","https://openalex.org/W2011999472","https://openalex.org/W2016984768","https://openalex.org/W2032159439","https://openalex.org/W2034348415","https://openalex.org/W2038699153","https://openalex.org/W2042179241","https://openalex.org/W2042426695","https://openalex.org/W2054459484","https://openalex.org/W2055257826","https://openalex.org/W2055982472","https://openalex.org/W2059155916","https://openalex.org/W2059661411","https://openalex.org/W2074863496","https://openalex.org/W2078908612","https://openalex.org/W2088617781","https://openalex.org/W2099755197","https://openalex.org/W2120934134","https://openalex.org/W2124064239","https://openalex.org/W2132339863","https://openalex.org/W2135412646","https://openalex.org/W2139594840","https://openalex.org/W2148061022","https://openalex.org/W2167816765","https://openalex.org/W2170820578","https://openalex.org/W2771332986","https://openalex.org/W2782758897","https://openalex.org/W2907088218","https://openalex.org/W2945210857","https://openalex.org/W2966785732","https://openalex.org/W2983120862","https://openalex.org/W3123313514","https://openalex.org/W3198334079","https://openalex.org/W4205296686","https://openalex.org/W4210817330","https://openalex.org/W4231235429","https://openalex.org/W4294232669","https://openalex.org/W4300926135","https://openalex.org/W4323658982"],"related_works":["https://openalex.org/W2506111601","https://openalex.org/W2766044635","https://openalex.org/W2943988667","https://openalex.org/W4300757011","https://openalex.org/W2981995226","https://openalex.org/W2489438003","https://openalex.org/W2493913654","https://openalex.org/W2102467404","https://openalex.org/W4387619756","https://openalex.org/W2608536130"],"abstract_inverted_index":{"Abstract":[0],"The":[1,86,133],"geodesic":[2,20,31,49,95,134,143,163,183,195],"edge":[3,26,50,135,165,184],"center":[4,51,97,136,185],"of":[5,27,52,98,147,181],"a":[6,10,43,48,53,99,178,189],"simple":[7,54,100],"polygon":[8,15,101,202],"is":[9,33,157],"point":[11],"c":[12,23],"inside":[13,38],"the":[14,18,28,34,39,59,94,142,148,162,194,201],"that":[16,151],"minimizes":[17],"maximum":[19],"distance":[21,32,37],"from":[22,141],"to":[24,46,92,103,116,192,200],"any":[25],"polygon,":[29],"where":[30],"shortest":[35],"path":[36],"polygon.":[40,55,149],"We":[41],"give":[42,188],"linear-time":[44,190],"algorithm":[45,76,87,91,191],"find":[47,93,193],"This":[56],"improves":[57],"on":[58,83,89],"previous":[60],"$$O(n":[61],"\\log":[62],"n)$$":[63],"<mml:math":[64],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[65],"<mml:mrow>":[66],"<mml:mi>O</mml:mi>":[67],"<mml:mo>(</mml:mo>":[68],"<mml:mi>n</mml:mi>":[69,71],"<mml:mo>log</mml:mo>":[70],"<mml:mo>)</mml:mo>":[72],"</mml:mrow>":[73],"</mml:math>":[74],"time":[75,118,156],"by":[77,119],"Lubiw":[78],"and":[79,106,113,126],"Naredla":[80],"[European":[81],"Symposium":[82],"Algorithms,":[84],"2021].":[85],"builds":[88],"an":[90,114,158],"vertex":[96],"due":[102],"Pollack,":[104],"Sharir,":[105],"Rote":[107],"[Discrete":[108,128],"&amp;":[109,129],"Computational":[110,130],"Geometry,":[111,131],"1989]":[112],"improvement":[115],"linear":[117,155,175],"Ahn,":[120],"Barba,":[121],"Bose,":[122],"De":[123],"Carufel,":[124],"Korman,":[125],"Oh":[127],"2016].":[132],"can":[137,171],"easily":[138],"be":[139,172],"found":[140,173],"farthest-edge":[144,196],"Voronoi":[145,152,166,197],"diagram":[146,153,167,198],"Finding":[150],"in":[154,174],"open":[159],"question,":[160],"although":[161],"nearest":[164],"(the":[168],"medial":[169],"axis)":[170],"time.":[176],"As":[177],"first":[179],"step":[180],"our":[182],"algorithm,":[186],"we":[187],"restricted":[199],"boundary.":[203]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}