{"id":"https://openalex.org/W2273922064","doi":"https://doi.org/10.1142/s1793830916500269","title":"A new algorithm for enumerating all possible Sudoku squares","display_name":"A new algorithm for enumerating all possible Sudoku squares","publication_year":2016,"publication_date":"2016-02-16","ids":{"openalex":"https://openalex.org/W2273922064","doi":"https://doi.org/10.1142/s1793830916500269","mag":"2273922064"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830916500269","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500269","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and 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":null,"display_name":"Pallavi Mishra","orcid":null},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pallavi Mishra","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101608029","display_name":"D. K. Gupta","orcid":"https://orcid.org/0009-0005-9776-7404"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"D. K. Gupta","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015249689","display_name":"Rakesh P. Badoni","orcid":"https://orcid.org/0000-0003-4383-6652"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rakesh P. Badoni","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, West Bengal, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.186,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55179566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"08","issue":"02","first_page":"1650026","last_page":"1650026"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.98580002784729,"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/T11130","display_name":"Coding theory and cryptography","score":0.9470000267028809,"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/disjoint-sets","display_name":"Disjoint sets","score":0.7417658567428589},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7109727263450623},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6780351400375366},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6304211616516113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6096532940864563},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.511945366859436},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5033738017082214},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.49835991859436035},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4903564453125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46199846267700195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33920764923095703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2567773759365082}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7417658567428589},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7109727263450623},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6780351400375366},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6304211616516113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6096532940864563},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.511945366859436},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5033738017082214},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.49835991859436035},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4903564453125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46199846267700195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33920764923095703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2567773759365082},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830916500269","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500269","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1534203014","https://openalex.org/W1970454743","https://openalex.org/W2006034008","https://openalex.org/W2015751597","https://openalex.org/W2026263015","https://openalex.org/W2027301459","https://openalex.org/W2068508408","https://openalex.org/W2083140445","https://openalex.org/W2089456700","https://openalex.org/W2098386829","https://openalex.org/W2099112283","https://openalex.org/W2128919229","https://openalex.org/W2142229742","https://openalex.org/W2402297725","https://openalex.org/W2962953495","https://openalex.org/W4255911649"],"related_works":["https://openalex.org/W2404647514","https://openalex.org/W4247536566","https://openalex.org/W1667647204","https://openalex.org/W132109778","https://openalex.org/W1989984537","https://openalex.org/W2499670206","https://openalex.org/W2072510267","https://openalex.org/W2924623028","https://openalex.org/W4288411600","https://openalex.org/W1525049041"],"abstract_inverted_index":{"Sudoku":[0,127,158,259],"is":[1,85,117,135,153,217,223,248,255,267,272],"an":[2,21],"interesting":[3],"number":[4,237],"placement":[5],"puzzle":[6,19,80,109],"with":[7],"some":[8,12,65,185],"simple":[9],"rules.":[10],"For":[11],"positive":[13],"integer":[14],"[Formula:":[15,22,28,36,43,47,91,95,131,144,199,228,242,263],"see":[16,23,29,37,44,48,92,96,132,145,200,225,229,243,264],"text],":[17,226],"the":[18,41,62,75,79,83,88,99,105,108,138,161,178,195,215,235,239,252,258],"involves":[20],"text]":[24,30,38,45,49,93,97,146,201,244],"grid":[25,102],"partitioned":[26],"into":[27],"distinct":[31],"blocks":[32],"each":[33,54,56,59,172,210],"of":[34,61,107,114,129,140,163,180,197,202,214,238,241,261,279],"size":[35,130,262],"such":[39,103],"that":[40,104,269],"integers":[42],"through":[46],"appear":[50],"exactly":[51],"once":[52],"in":[53,78,98,277],"row,":[55],"column":[57],"and":[58,81,160,191,275],"block":[60],"grid.":[63],"Often":[64],"static":[66],"numbers":[67,89],"known":[68],"as":[69,150,189],"givens":[70],"are":[71,110,168,206],"placed":[72],"according":[73],"to":[74,86,94,118,171,209],"difficulty":[76],"rating":[77],"then":[82,192],"rule":[84],"place":[87],"from":[90,143],"partially":[100],"filled":[101],"conditions":[106],"satisfied.":[111],"The":[112,174,212],"aim":[113],"this":[115],"paper":[116],"propose":[119],"a":[120,154],"new":[121],"algorithm":[122,176,188,216,254,271],"for":[123,257],"enumerating":[124],"all":[125,181,194,203],"possible":[126],"squares":[128,159,260],"text].":[133,230,265],"It":[134,266],"based":[136],"on":[137],"concepts":[139],"permutations":[141],"derived":[142],"S-permutation":[147,165],"matrices":[148,166],"termed":[149],"S-permutations.":[151],"There":[152],"one-to-one":[155],"correspondence":[156],"between":[157],"set":[162,179],"those":[164],"which":[167,205],"mutually":[169,207,245],"disjoint":[170,208,246],"other.":[173,211],"proposed":[175,253],"uses":[177],"S-permutations":[182,204,247],"generated":[183],"by":[184],"permutation":[186],"generation":[187],"input":[190],"enumerates":[193],"subsets":[196],"cardinality":[198],"correctness":[213],"established.":[218],"Its":[219],"worst-case":[220],"time":[221],"complexity":[222],"O[Formula:":[224],"where":[227],"A":[231],"mathematical":[232],"formula":[233],"involving":[234],"total":[236],"sets":[240],"also":[249],"derived.":[250],"Experimentally,":[251],"verified":[256],"observed":[268],"our":[270],"more":[273],"systematic":[274],"better":[276],"terms":[278],"computational":[280],"efficiency.":[281]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}