{"id":"https://openalex.org/W2260781372","doi":"https://doi.org/10.1587/transfun.e97.a.1213","title":"Computational Complexity and an Integer Programming Model of Shakashaka","display_name":"Computational Complexity and an Integer Programming Model of Shakashaka","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2260781372","doi":"https://doi.org/10.1587/transfun.e97.a.1213","mag":"2260781372"},"language":"en","primary_location":{"id":"doi:10.1587/transfun.e97.a.1213","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.e97.a.1213","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","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/A5083684609","display_name":"Erik D. Demaine","orcid":"https://orcid.org/0000-0003-3803-5703"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erik D. DEMAINE","raw_affiliation_strings":["MIT Computer Science and Artificial Intelligence Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT Computer Science and Artificial Intelligence Laboratory","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080521209","display_name":"Yoshio Okamoto","orcid":"https://orcid.org/0000-0002-9826-7074"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshio OKAMOTO","raw_affiliation_strings":["Graduate School of Informatics and Engineering, The University of Electro-Communications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Informatics and Engineering, The University of Electro-Communications","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054829031","display_name":"Ryuhei Uehara","orcid":"https://orcid.org/0000-0003-0895-3765"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryuhei UEHARA","raw_affiliation_strings":["School of Information Science, JAIST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science, JAIST","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062599134","display_name":"Yushi Uno","orcid":null},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yushi UNO","raw_affiliation_strings":["Graduate School of Science, Osaka Prefecture University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science, Osaka Prefecture University","institution_ids":["https://openalex.org/I15807432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4851,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.91363334,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"E97.A","issue":"6","first_page":"1213","last_page":"1219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9570000171661377,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/integer-programming","display_name":"Integer programming","score":0.729295015335083},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6465637683868408},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6255768537521362},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5654805898666382},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.5541518926620483},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4789041578769684},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42524251341819763},{"id":"https://openalex.org/keywords/problem-solver","display_name":"Problem solver","score":0.41457849740982056},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32644128799438477},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.19023579359054565},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.12416708469390869},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07323867082595825}],"concepts":[{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.729295015335083},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6465637683868408},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6255768537521362},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5654805898666382},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.5541518926620483},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4789041578769684},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42524251341819763},{"id":"https://openalex.org/C3019612716","wikidata":"https://www.wikidata.org/wiki/Q730920","display_name":"Problem solver","level":2,"score":0.41457849740982056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32644128799438477},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.19023579359054565},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.12416708469390869},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07323867082595825},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1587/transfun.e97.a.1213","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.e97.a.1213","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3552538742","display_name":null,"funder_award_id":"24106004","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4152892095","display_name":"Mathematical Approaches to Reliable Exact Computation and Its Theoretical Guarantee","funder_award_id":"24700008","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7950758475","display_name":"Research on geometric folding algorithms","funder_award_id":"26330009","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8196568000","display_name":null,"funder_award_id":"24106005","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W600955335","https://openalex.org/W1545736378","https://openalex.org/W1974709582","https://openalex.org/W2014328192","https://openalex.org/W2066577300","https://openalex.org/W2091345559","https://openalex.org/W2128356007","https://openalex.org/W2130564774","https://openalex.org/W2186604801","https://openalex.org/W4214952174"],"related_works":["https://openalex.org/W2132874577","https://openalex.org/W1836984851","https://openalex.org/W2011621332","https://openalex.org/W2116898168","https://openalex.org/W1605093979","https://openalex.org/W2152572054","https://openalex.org/W2920969592","https://openalex.org/W2074269745","https://openalex.org/W2568362682","https://openalex.org/W2990609819"],"abstract_inverted_index":{"Shakashaka":[0,25,41],"is":[1,26,36],"a":[2,61],"pencil-and-paper":[3],"puzzle":[4],"proposed":[5],"by":[6,10,22],"Guten":[7],"and":[8,28,47],"popularized":[9],"the":[11,19,32],"Japanese":[12],"publisher":[13],"Nikoli":[14],"(like":[15],"Sudoku).":[16],"We":[17],"determine":[18],"computational":[20],"complexity":[21],"proving":[23],"that":[24,30,49],"NP-complete,":[27],"furthermore":[29],"counting":[31],"number":[33],"of":[34],"solutions":[35],"#P-complete.":[37],"Next":[38],"we":[39],"formulate":[40],"as":[42],"an":[43,50],"integer-programming":[44],"(IP)":[45],"problem,":[46],"show":[48],"IP":[51],"solver":[52],"can":[53],"solve":[54],"every":[55],"instance":[56],"from":[57],"Nikoli's":[58],"website":[59],"within":[60],"second.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
