{"id":"https://openalex.org/W2528535737","doi":"https://doi.org/10.1142/s021819591860004x","title":"Reconstruction of Weakly Simple Polygons from Their Edges","display_name":"Reconstruction of Weakly Simple Polygons from Their Edges","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2528535737","doi":"https://doi.org/10.1142/s021819591860004x","mag":"2528535737"},"language":"en","primary_location":{"id":"doi:10.1142/s021819591860004x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819591860004x","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.00361","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hugo A. Akitaya","orcid":null},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hugo A. Akitaya","raw_affiliation_strings":["Department of Computer Science, Tufts University, 161 College Ave., Medford, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Tufts University, 161 College Ave., Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"last","author":{"id":null,"display_name":"Csaba D. T\u00f3th","orcid":null},"institutions":[{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":["Department of Mathematics, California State University Northridge, 18111 Nordhoff St., Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, California State University Northridge, 18111 Nordhoff St., Los Angeles, CA, USA","institution_ids":["https://openalex.org/I157638225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.00791506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"02","first_page":"161","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9587000012397766,"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":0.9587000012397766,"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":0.012000000104308128,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/simple-polygon","display_name":"Simple polygon","score":0.7734000086784363},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7383000254631042},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.6934000253677368},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.6527000069618225},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.6419000029563904},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.4426000118255615},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.4374000132083893},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.40939998626708984}],"concepts":[{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.7734000086784363},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7383000254631042},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7186999917030334},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.6934000253677368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6762999892234802},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6527000069618225},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.6419000029563904},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.4374000132083893},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.38040000200271606},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.3700999915599823},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C1449246","wikidata":"https://www.wikidata.org/wiki/Q7936080","display_name":"Visibility polygon","level":4,"score":0.3212999999523163},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3070000112056732},{"id":"https://openalex.org/C59902600","wikidata":"https://www.wikidata.org/wiki/Q1575331","display_name":"Point in polygon","level":3,"score":0.3034000098705292},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2831999957561493},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s021819591860004x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819591860004x","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1610.00361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00361","pdf_url":"https://arxiv.org/pdf/1610.00361","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.00361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00361","pdf_url":"https://arxiv.org/pdf/1610.00361","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5576055045","display_name":null,"funder_award_id":"CCF-1423615","funder_id":"https://openalex.org/F4320332169","funder_display_name":"Directorate for Computer and Information Science and Engineering"},{"id":"https://openalex.org/G8573991905","display_name":null,"funder_award_id":"CCF-1422311","funder_id":"https://openalex.org/F4320332169","funder_display_name":"Directorate for Computer and Information Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W14598044","https://openalex.org/W1973343935","https://openalex.org/W2022451101","https://openalex.org/W2027854745","https://openalex.org/W2028883079","https://openalex.org/W2031165997","https://openalex.org/W2048707633","https://openalex.org/W2069950735","https://openalex.org/W2106413026","https://openalex.org/W2115754974","https://openalex.org/W2127145740","https://openalex.org/W2309657040","https://openalex.org/W4213252030","https://openalex.org/W4251391716"],"related_works":[],"abstract_inverted_index":{"We":[0,63,99,135,199],"address":[1],"the":[2,9,21,46,66,116,127,131,140,143,146,165,186],"problem":[3,47,67],"of":[4,11,145,168,190],"reconstructing":[5,106],"a":[6,24,60,76,96,173,195],"polygon":[7,25,58,77],"from":[8],"multiset":[10],"its":[12],"edges.":[13],"Given":[14],"[Formula:":[15,27,49,86,91,101,147],"see":[16,28,50,87,92,102,148],"text]":[17,29,51,149],"line":[18,180],"segments":[19,112,132,151,181,192],"in":[20,48,120,129],"plane,":[22],"find":[23,164,185],"with":[26],"vertices":[30,79],"whose":[31,78],"edges":[32],"are":[33,113,119,133],"these":[34],"segments,":[35,163],"or":[36,59,115],"report":[37],"that":[38,65,74,142,193],"none":[39],"exists.":[40],"It":[41],"is":[42,68,152],"easy":[43],"to":[44,94,126,171],"solve":[45],"time":[52],"if":[53],"we":[54],"seek":[55],"an":[56],"arbitrary":[57],"simple":[61,72,97,108,175,197],"polygon.":[62,98,176,198],"show":[64],"NP-complete":[69],"for":[70,89,105,139,206],"weakly":[71,107,174,196],"polygons,":[73],"is,":[75],"can":[80,158,182],"be":[81,159,183],"perturbed":[82],"by":[83],"at":[84],"most":[85],"text],":[88,93],"any":[90],"obtain":[95],"give":[100,200],"text]-time":[103],"algorithms":[104],"polygons:":[109],"when":[110],"all":[111],"collinear":[114],"segment":[117,157],"endpoints":[118],"general":[121],"position.":[122],"These":[123],"results":[124],"extend":[125],"variant":[128],"which":[130],"directed.":[134],"study":[136],"related":[137],"problems":[138],"case":[141],"union":[144],"input":[150],"connected.":[153],"(i)":[154],"If":[155,178],"each":[156],"subdivided":[160],"into":[161],"several":[162],"minimum":[166,187],"number":[167],"subdivision":[169],"points":[170],"form":[172],"(ii)":[177],"new":[179,191],"added,":[184],"total":[188],"length":[189],"creates":[194],"worst-case":[201],"upper":[202],"and":[203],"lower":[204],"bounds":[205],"both":[207],"problems.":[208]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-10-14T00:00:00"}
