{"id":"https://openalex.org/W2097185467","doi":"https://doi.org/10.1051/ita:2007046","title":"Computing the<i>j</i>th solution of a first-order query","display_name":"Computing the<i>j</i>th solution of a first-order query","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2097185467","doi":"https://doi.org/10.1051/ita:2007046","mag":"2097185467"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2007046","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007046","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics 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":"https://openalex.org/A5078697158","display_name":"Guillaume Bagan","orcid":null},"institutions":[{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Guillaume Bagan","raw_affiliation_strings":["GREYC, Universit\u00e9 de Caen, ENSICAEN, CNRS, Campus 2, 14032 Caen Cedex, France; gbagan@info.unicaen.fr; grandjean@info.unicaen.fr"],"affiliations":[{"raw_affiliation_string":"GREYC, Universit\u00e9 de Caen, ENSICAEN, CNRS, Campus 2, 14032 Caen Cedex, France; gbagan@info.unicaen.fr; grandjean@info.unicaen.fr","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059509786","display_name":"Arnaud Durand","orcid":"https://orcid.org/0000-0002-7629-2121"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud Durand","raw_affiliation_strings":["\u00c9quipe de Logique Math\u00e9matique, Universit\u00e9 Denis Diderot, CNRS UMR 7056, 2 place Jussieu, 75251 Paris Cedex 05, France; durand@logique.jussieu.fr"],"affiliations":[{"raw_affiliation_string":"\u00c9quipe de Logique Math\u00e9matique, Universit\u00e9 Denis Diderot, CNRS UMR 7056, 2 place Jussieu, 75251 Paris Cedex 05, France; durand@logique.jussieu.fr","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008969654","display_name":"\u00c9tienne Grandjean","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Etienne Grandjean","raw_affiliation_strings":["GREYC, Universit\u00e9 de Caen, ENSICAEN, CNRS, Campus 2, 14032 Caen Cedex, France; gbagan@info.unicaen.fr; grandjean@info.unicaen.fr"],"affiliations":[{"raw_affiliation_string":"GREYC, Universit\u00e9 de Caen, ENSICAEN, CNRS, Campus 2, 14032 Caen Cedex, France; gbagan@info.unicaen.fr; grandjean@info.unicaen.fr","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025043872","display_name":"Fr\u00e9d\u00e9ric Olive","orcid":"https://orcid.org/0000-0002-3552-5566"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Olive","raw_affiliation_strings":["LIF, Universit\u00e9 Aix-Marseille 1, CNRS, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France; frederic.olive@lif.univ-mrs.fr"],"affiliations":[{"raw_affiliation_string":"LIF, Universit\u00e9 Aix-Marseille 1, CNRS, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France; frederic.olive@lif.univ-mrs.fr","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078697158"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I98702875"],"apc_list":null,"apc_paid":null,"fwci":0.4005,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.67918508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"42","issue":"1","first_page":"147","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/lexicographical-order","display_name":"Lexicographical order","score":0.7386419773101807},{"id":"https://openalex.org/keywords/precomputation","display_name":"Precomputation","score":0.6868957281112671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6613961458206177},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6530344486236572},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5830278396606445},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5617809295654297},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5543439388275146},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5186406970024109},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.46175432205200195},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.46064096689224243},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44624701142311096},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30700284242630005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18476980924606323},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.11807829141616821}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7386419773101807},{"id":"https://openalex.org/C159379195","wikidata":"https://www.wikidata.org/wiki/Q7239568","display_name":"Precomputation","level":3,"score":0.6868957281112671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6613961458206177},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6530344486236572},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5830278396606445},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5617809295654297},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5543439388275146},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5186406970024109},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.46175432205200195},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.46064096689224243},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44624701142311096},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30700284242630005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18476980924606323},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.11807829141616821},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita:2007046","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007046","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2008__42_1_147_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2007046/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W891461","https://openalex.org/W52840101","https://openalex.org/W193724012","https://openalex.org/W1489366126","https://openalex.org/W1573632260","https://openalex.org/W1579803282","https://openalex.org/W1588422895","https://openalex.org/W1964905213","https://openalex.org/W1993920925","https://openalex.org/W2004485491","https://openalex.org/W2022112486","https://openalex.org/W2030076354","https://openalex.org/W2031641275","https://openalex.org/W2041198634","https://openalex.org/W2046652577","https://openalex.org/W2048685245","https://openalex.org/W2295428206","https://openalex.org/W4231916799"],"related_works":["https://openalex.org/W126258643","https://openalex.org/W2157769033","https://openalex.org/W2096978683","https://openalex.org/W2687399516","https://openalex.org/W2543067032","https://openalex.org/W414359703","https://openalex.org/W3029113864","https://openalex.org/W2488395346","https://openalex.org/W87953084","https://openalex.org/W1534826865"],"abstract_inverted_index":{"We":[0],"design":[1],"algorithms":[2],"of":[3,16,46,105,114,132,140,147,152,158,210],"\u201coptimal\"":[4],"data":[5,116],"complexity":[6,117,204],"for":[7,120,148,167,201],"several":[8,47,64],"natural":[9],"problems":[10,33],"about":[11],"first-order":[12,126,211],"queries":[13],"on":[14,213],"structures":[15],"bounded":[17,133],"degree.":[18],"For":[19],"that":[20],"purpose,":[21],"we":[22,164],"first":[23],"introduce":[24],"a":[25,62,68,137,194,207],"framework":[26],"to":[27,60],"deal":[28],"with":[29,190],"logical":[30],"or":[31],"combinatorial":[32],"R":[34],"\u2282":[35],"I":[36,43],"x":[37,41],"O":[38,53],"whose":[39],"instances":[40],"\u2208":[42,52,56,77],"may":[44],"admit":[45],"solutions":[48],"R(x)":[49,98],"=":[50,99],"{y":[51],":":[54],"(x,y)":[55],"R}.":[57],"One":[58],"associates":[59],"such":[61],"problem":[63,174],"specific":[65,87],"tasks:":[66],"compute":[67,101,136,143],"random":[69,138],"(for":[70],"the":[71,102,109,121,144,156,172],"uniform":[72],"probability":[73],"distribution)":[74],"solution":[75,83,103],"y":[76],"R(x);":[78],"enumerate":[79,155],"without":[80],"repetition":[81],"each":[82],"yj":[84,104],"in":[85,108,159],"some":[86,149],"linear":[88,110,150,195],"order":[89,111,151],"y0":[90],"<":[91,93,95],"y1":[92],"...":[94],"yn-1":[96],"where":[97],"{y0,...,yn-1};":[100],"rank":[106],"j":[107],"<.":[112],"Algorithms":[113],"\u201cminimal\"":[115],"are":[118],"presented":[119],"following":[122],"problems:":[123],"given":[124],"any":[125,129,168],"formula":[127,170],"and":[128],"structure":[130],"S":[131],"degree:":[134],"(1)":[135,175],"element":[139,146],";":[141,153],"(2)":[142],"jth":[145],"(3)":[154],"elements":[157],"lexicographical":[160],"order.":[161],"More":[162],"precisely,":[163],"prove":[165],"that,":[166],"fixed":[169],"\u03c6,":[171],"above":[173],"(resp.":[176,186],"(2),":[177],"(3))":[178],"can":[179],"be":[180],"computed":[181],"within":[182,187],"average":[183],"constant":[184,188,191],"time":[185],"time,":[189],"delay)":[192],"after":[193],"(O(|S|))":[196],"precomputation.":[197],"Our":[198],"essential":[199],"tool":[200],"deriving":[202],"those":[203],"results":[205],"is":[206],"normalization":[208],"procedure":[209],"formulas":[212],"bijective":[214],"structures.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}