{"id":"https://openalex.org/W2160751058","doi":"https://doi.org/10.1142/s0218195993000282","title":"P-COMPLETE GEOMETRIC PROBLEMS","display_name":"P-COMPLETE GEOMETRIC PROBLEMS","publication_year":1993,"publication_date":"1993-12-01","ids":{"openalex":"https://openalex.org/W2160751058","doi":"https://doi.org/10.1142/s0218195993000282","mag":"2160751058"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195993000282","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195993000282","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113562454","display_name":"Mikhail J. Atallah","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MIKHAIL J. ATALLAH","raw_affiliation_strings":["Dept. of Computer Sciences, Purdue Univ., W. Lafayette, IN 47907, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Sciences, Purdue Univ., W. Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062115294","display_name":"Paul B. Callahan","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"PAUL B. CALLAHAN","raw_affiliation_strings":["Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034971300","display_name":"Michael T. Goodrich","orcid":"https://orcid.org/0000-0002-8943-191X"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MICHAEL T. GOODRICH","raw_affiliation_strings":["Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113562454"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":0.3905,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.64548023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"03","issue":"04","first_page":"443","last_page":"462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"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":0.9987000226974487,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9878000020980835,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.97079998254776,"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/polygon","display_name":"Polygon (computer graphics)","score":0.8049404621124268},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7864331007003784},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.747785747051239},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.6531445980072021},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6162452697753906},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5101063847541809},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4713696241378784},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.45698219537734985},{"id":"https://openalex.org/keywords/covering-problems","display_name":"Covering problems","score":0.4252944886684418},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35047847032546997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19862687587738037},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1913112998008728},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.08135652542114258}],"concepts":[{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.8049404621124268},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7864331007003784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.747785747051239},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6531445980072021},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6162452697753906},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5101063847541809},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4713696241378784},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.45698219537734985},{"id":"https://openalex.org/C103646786","wikidata":"https://www.wikidata.org/wiki/Q5179260","display_name":"Covering problems","level":3,"score":0.4252944886684418},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35047847032546997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19862687587738037},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1913112998008728},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.08135652542114258},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195993000282","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195993000282","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.44999998807907104,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W768569191","https://openalex.org/W4206327962","https://openalex.org/W4301895170","https://openalex.org/W2163760347","https://openalex.org/W2963936214","https://openalex.org/W2610026222","https://openalex.org/W4241226487","https://openalex.org/W2358728421","https://openalex.org/W2466150543","https://openalex.org/W2355806726"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,30,48],"show":[4],"that":[5,35],"it":[6],"is":[7],"impossible":[8],"to":[9],"solve":[10],"a":[11,22,32],"number":[12,24],"of":[13,25,52],"\u201cnatural\u201d":[14],"two-dimensional":[15],"geometric":[16,41,58],"problems":[17,42,47],"in":[18,43],"polylog":[19],"time":[20],"with":[21],"polynomial":[23],"processors":[26],"(unless":[27],"P=NC).":[28],"Thus,":[29],"disprove":[31],"popular":[33],"belief":[34],"there":[36],"are":[37,62],"no":[38],"natural":[39],"P-complete":[40],"the":[44,68],"plane.":[45],"The":[46],"address":[49],"include":[50],"instances":[51],"polygon":[53],"triangulation,":[54],"planar":[55,73],"partitioning,":[56],"and":[57,72],"layering.":[59],"Our":[60],"results":[61],"based":[63],"on":[64],"non-trivial":[65],"reductions":[66],"from":[67],"monotone":[69],"circuit":[70,74],"value":[71,75],"problems.":[76]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
