{"id":"https://openalex.org/W2140515217","doi":"https://doi.org/10.1137/0209028","title":"On the Polyhedral Decision Problem","display_name":"On the Polyhedral Decision Problem","publication_year":1980,"publication_date":"1980-05-01","ids":{"openalex":"https://openalex.org/W2140515217","doi":"https://doi.org/10.1137/0209028","mag":"2140515217"},"language":"en","primary_location":{"id":"doi:10.1137/0209028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209028","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5076560802","display_name":"Andrew Chi-Chih Yao","orcid":"https://orcid.org/0000-0002-3648-5594"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrew C. Yao","raw_affiliation_strings":["$ Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","\" Computer Science Department, Stanford University, Stanford, California 94305"],"affiliations":[{"raw_affiliation_string":"$ Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"\" Computer Science Department, Stanford University, Stanford, California 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051087399","display_name":"Ronald L. Rivest","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald L. Rivest","raw_affiliation_strings":["$ Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","\" Computer Science Department, Stanford University, Stanford, California 94305"],"affiliations":[{"raw_affiliation_string":"$ Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"\" Computer Science Department, Stanford University, Stanford, California 94305","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076560802"],"corresponding_institution_ids":["https://openalex.org/I63966007","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":8.168,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.97657082,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"2","first_page":"343","last_page":"347"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9835000038146973,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.5117614269256592},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4344662129878998},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3996114134788513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3660343289375305},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21688055992126465}],"concepts":[{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.5117614269256592},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4344662129878998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3996114134788513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3660343289375305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21688055992126465}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0209028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209028","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.309.9198","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.9198","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.csail.mit.edu/rivest/pubs/YR80.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7799999713897705}],"awards":[{"id":"https://openalex.org/G6146296403","display_name":null,"funder_award_id":"MCS-77","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W30254118","https://openalex.org/W1494436834","https://openalex.org/W1963956809","https://openalex.org/W2028627293","https://openalex.org/W2032324603","https://openalex.org/W2105310556"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Computational":[0],"problems":[1],"sometimes":[2],"can":[3],"be":[4],"cast":[5],"in":[6,15,23,52,73],"the":[7,37,53,75],"following":[8],"form:":[9],"Given":[10],"a":[11,32],"point":[12],"${\\bf":[13,20],"x}$":[14,21],"$R^n":[16],"$,":[17],"determine":[18],"if":[19],"lies":[22],"some":[24],"fixed":[25],"polyhedron.":[26],"In":[27],"this":[28,67],"paper":[29],"we":[30],"give":[31],"general":[33],"lower":[34,70],"bound":[35],"to":[36,69],"complexity":[38],"of":[39,77],"such":[40],"problems,":[41],"showing":[42],"that":[43],"$\\frac{1}{2}\\log":[44],"_2":[45],"f_s":[46],"$":[47],"linear":[48],"comparisons":[49],"are":[50],"needed":[51],"worst":[54],"case,":[55],"for":[56],"any":[57],"polyhedron":[58],"with":[59,64],"$f_s$s-dimensional":[60],"faces.":[61],"For":[62],"polyhedra":[63],"abundant":[65],"faces,":[66],"leads":[68],"bounds":[71],"nonlinear":[72],"n,":[74],"number":[76],"variables.":[78]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}