{"id":"https://openalex.org/W2949127580","doi":"https://doi.org/10.20382/jocg.v11i2a9","title":"Convex polygons in cartesian products","display_name":"Convex polygons in cartesian products","publication_year":2021,"publication_date":"2021-02-11","ids":{"openalex":"https://openalex.org/W2949127580","doi":"https://doi.org/10.20382/jocg.v11i2a9","mag":"2949127580"},"language":"en","primary_location":{"id":"pmh:oai:pure.tue.nl:openaire/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"De Carufel, J-L, Dumitrescu, A, Meulemans, W, Ophelders, T, Pennarun, C, T\u00f3th, C D & Verdonschot, S 2021, 'Convex polygons in Cartesian products', Journal of Computational Geometry, vol. 11, no. 2, pp. 205-233. https://doi.org/10.20382/jocg.v11i2a9","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"preprint","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.tue.nl/en/publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042440491","display_name":"Jean-Lou De Carufel","orcid":"https://orcid.org/0000-0002-6734-8234"},"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":"De Carufel, Jean-Lou","raw_affiliation_strings":["Carleton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carleton University","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091313409","display_name":"Adrian Dumitrescu","orcid":"https://orcid.org/0000-0002-1118-0321"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dumitrescu, Adrian","raw_affiliation_strings":["Department of Computer Sciences [Madison]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences [Madison]","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062614232","display_name":"Wouter Meulemans","orcid":"https://orcid.org/0000-0002-4978-3400"},"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":"Meulemans, Wouter","raw_affiliation_strings":["Eindhoven University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013950801","display_name":"Tim Ophelders","orcid":"https://orcid.org/0000-0002-9570-024X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ophelders, Tim","raw_affiliation_strings":["Department of Mathematics and Computer Science [Eindhoven]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science [Eindhoven]","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029498919","display_name":"Claire Pennarun","orcid":"https://orcid.org/0000-0002-9895-3437"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pennarun, Claire","raw_affiliation_strings":["Algorithmes, Graphes et Combinatoire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithmes, Graphes et Combinatoire","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T\u00f3th, Csaba D","raw_affiliation_strings":["Department of Computer Science [Calgary]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science [Calgary]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074370405","display_name":"Sander Verdonschot","orcid":"https://orcid.org/0000-0002-7892-2561"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Verdonschot, Sander","raw_affiliation_strings":["School of Computer Science (Carleton, Ottawa)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science (Carleton, Ottawa)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"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":0.00624675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":1.0,"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":1.0,"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":0.998199999332428,"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/T12288","display_name":"Optimization and Search Problems","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/regular-polygon","display_name":"Regular polygon","score":0.6012184023857117},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.509077250957489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4601157307624817},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.4372698664665222},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3991115987300873},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30999836325645447}],"concepts":[{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6012184023857117},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.509077250957489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4601157307624817},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.4372698664665222},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3991115987300873},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30999836325645447}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:pure.tue.nl:openaire/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"De Carufel, J-L, Dumitrescu, A, Meulemans, W, Ophelders, T, Pennarun, C, T\u00f3th, C D & Verdonschot, S 2021, 'Convex polygons in Cartesian products', Journal of Computational Geometry, vol. 11, no. 2, pp. 205-233. https://doi.org/10.20382/jocg.v11i2a9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ojs.library.carleton.ca:article/3124","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3124","pdf_url":"https://jocg.org/index.php/jocg/article/view/3124","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 2: Special Issue of Selected Papers from SoCG 2019; 205\u2013233","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e5e52059be514fe9b7e61a5d9a8317bd","is_oa":true,"landing_page_url":"https://doaj.org/article/e5e52059be514fe9b7e61a5d9a8317bd","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 11, Iss 2 (2021)","raw_type":"article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"Journal of Computational Geometry, 11(2), 205 - 233. Macodrum library, Carleton University","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.20382/jocg.v11i2a9","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v11i2a9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:openaire/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/205b6d5f-dfdf-4712-b3e9-994177b0f8f6","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"De Carufel, J-L, Dumitrescu, A, Meulemans, W, Ophelders, T, Pennarun, C, T\u00f3th, C D & Verdonschot, S 2021, 'Convex polygons in Cartesian products', Journal of Computational Geometry, vol. 11, no. 2, pp. 205-233. https://doi.org/10.20382/jocg.v11i2a9","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W62593040","https://openalex.org/W103607126","https://openalex.org/W202648750","https://openalex.org/W1966946221","https://openalex.org/W1971456489","https://openalex.org/W1998666916","https://openalex.org/W2003172399","https://openalex.org/W2012104218","https://openalex.org/W2022062611","https://openalex.org/W2033635232","https://openalex.org/W2038730428","https://openalex.org/W2039925482","https://openalex.org/W2041113155","https://openalex.org/W2057647747","https://openalex.org/W2083179104","https://openalex.org/W2091981456","https://openalex.org/W2094692117","https://openalex.org/W2108498688","https://openalex.org/W2108616329","https://openalex.org/W2110861431","https://openalex.org/W2112876384","https://openalex.org/W2142569580","https://openalex.org/W2143379314","https://openalex.org/W2404118392","https://openalex.org/W2510524578","https://openalex.org/W2964204159"],"related_works":["https://openalex.org/W2141418112","https://openalex.org/W2949097972","https://openalex.org/W4299640900","https://openalex.org/W2738565459","https://openalex.org/W3159629589","https://openalex.org/W2616059925","https://openalex.org/W2601112296","https://openalex.org/W1995409531","https://openalex.org/W3030274415","https://openalex.org/W68628300"],"abstract_inverted_index":{"We":[0,49,111],"study":[1],"several":[2],"problems":[3],"concerning":[4],"convex":[5,36,76,94,119,148],"polygons":[6],"whose":[7],"vertices":[8],"lie":[9],"in":[10,35,75,78,97,147,150],"a":[11,46,57,63,79,98,118,131],"Cartesian":[12],"product":[13],"of":[14,17,67,73,117,133,144],"two":[15,103],"sets":[16,146],"$n$":[18],"real":[19],"numbers":[20],"(for":[21,56],"short,":[22],"\\emph{grid}).":[23],"First,":[24],"we":[25,83,136],"prove":[26],"that":[27,39,100,113],"every":[28],"such":[29,122,151],"grid":[30,99],"contains":[31,101],"$\\Omega(\\log":[32],"n)$":[33],"points":[34,74,104],"position":[37,77,149],"and":[38,61,153],"this":[40,51],"bound":[41,66],"is":[42],"tight":[43,64,161],"up":[44,129,162],"to":[45,53,130,163],"constant":[47],"factor.":[48],"generalize":[50],"result":[52],"$d$":[54],"dimensions":[55],"fixed":[58],"$d\\in":[59],"\\mathbb{N}$),":[60],"obtain":[62],"lower":[65],"$\\Omega(\\log^{d-1}n)$":[68],"for":[69,87,154],"the":[70,89,106,114,141],"maximum":[71,115,142],"number":[72,143],"$d$-dimensional":[80],"grid.":[81],"Second,":[82],"present":[84,137],"polynomial-time":[85],"algorithms":[86],"computing":[88],"longest":[90],"x-":[91],"or":[92,109],"y-monotone":[93],"polygonal":[95],"chain":[96],"no":[102],"with":[105,121],"same":[107],"$x$-":[108],"$y$-coordinate.":[110],"show":[112],"size":[116],"polygon":[120],"unique":[123],"coordinates":[124],"can":[125],"be":[126],"efficiently":[127],"approximated":[128],"factor":[132],"$2$.":[134],"Finally,":[135],"exponential":[138],"bounds":[139,159],"on":[140],"point":[145],"grids,":[152],"some":[155],"restricted":[156],"variants.":[157],"These":[158],"are":[160],"polynomial":[164],"factors.":[165]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}