{"id":"https://openalex.org/W7163871092","doi":"https://doi.org/10.4230/lipics.swat.2026.7","title":"On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons","display_name":"On the Doubling Dimension and the Perimeter of Geodesically Convex Sets in Fat Polygons","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7163871092","doi":"https://doi.org/10.4230/lipics.swat.2026.7"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26043","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138158979","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":false,"raw_author_name":"de Berg, Mark","raw_affiliation_strings":["Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-5770-3784","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137171323","display_name":"Prosenjit Bose","orcid":"https://orcid.org/0000-0002-8906-0573"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bose, Prosenjit","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"raw_orcid":"https://orcid.org/0000-0002-8906-0573","affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000799434","display_name":"Leonidas Theocharous","orcid":"https://orcid.org/0000-0002-1707-6787"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Theocharous, Leonidas","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, University of Ottawa, Canada"],"raw_orcid":"https://orcid.org/0000-0002-1707-6787","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, University of Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.9670131,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.839900016784668,"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":0.839900016784668,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.020400000736117363,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.01140000019222498,"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":0.6696000099182129},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6432999968528748},{"id":"https://openalex.org/keywords/perimeter","display_name":"Perimeter","score":0.6136999726295471},{"id":"https://openalex.org/keywords/star-shaped-polygon","display_name":"Star-shaped polygon","score":0.5884000062942505},{"id":"https://openalex.org/keywords/point-in-polygon","display_name":"Point in polygon","score":0.5461000204086304},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5236999988555908},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.5022000074386597},{"id":"https://openalex.org/keywords/rectilinear-polygon","display_name":"Rectilinear polygon","score":0.4918999969959259},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4812999963760376}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7874000072479248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.718999981880188},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6696000099182129},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6432999968528748},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.6136999726295471},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.5884000062942505},{"id":"https://openalex.org/C59902600","wikidata":"https://www.wikidata.org/wiki/Q1575331","display_name":"Point in polygon","level":3,"score":0.5461000204086304},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5236999988555908},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.5022000074386597},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.4918999969959259},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4025999903678894},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.38449999690055847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37380000948905945},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.2639999985694885},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.25769999623298645}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26043","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.swat.2026.7","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.swat.2026.7","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26043","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"algorithmic":[1],"problems":[2,126],"can":[3],"be":[4],"solved":[5],"(almost)":[6],"as":[7,16],"efficiently":[8],"in":[9,17,27,93,144,153],"metric":[10,22],"spaces":[11],"of":[12,49,89,113,138,141],"bounded":[13,40,67,76],"doubling":[14,41,47,68,77],"dimension":[15,48,78],"Euclidean":[18,111],"space.":[19],"Unfortunately,":[20],"the":[21,33,46,87,110,114,135],"space":[23],"defined":[24],"by":[25],"points":[26,143],"a":[28,107,139],"simple":[29,61],"polygon":[30,73,147],"equipped":[31],"with":[32,97,148],"geodesic":[34],"distance":[35],"does":[36,74],"not":[37,64],"necessarily":[38],"have":[39,66,75],"dimension.":[42],"We":[43,57,84],"therefore":[44],"study":[45,86],"fat":[50],"polygons,":[51,129],"for":[52,124],"two":[53,118],"well-known":[54],"fatness":[55],"definitions.":[56],"prove":[58],"that":[59,101,133,151],"locally-fat":[60],"polygons":[62,95],"do":[63],"always":[65],"dimension,":[69],"while":[70],"any":[71],"(\u03b1,\u03b2)-covered":[72,94,128,146],"(even":[79],"if":[80],"it":[81],"has":[82],"holes).":[83],"also":[85],"perimeter":[88,103],"geodesically":[90],"convex":[91],"sets":[92],"(possibly":[96],"holes),":[98],"and":[99],"show":[100],"this":[102],"is":[104],"at":[105],"most":[106],"constant":[108],"times":[109],"diameter":[112],"set.":[115],"Using":[116],"these":[117],"results,":[119],"we":[120],"obtain":[121],"new":[122],"results":[123],"several":[125],"on":[127],"including":[130],"an":[131,145],"algorithm":[132],"computes":[134],"closest":[136],"pair":[137],"set":[140],"m":[142],"n":[149],"vertices":[150],"runs":[152],"O(n":[154],"+":[155],"mlog":[156],"n)":[157],"expected":[158],"time.":[159]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-06-09T00:00:00"}
