{"id":"https://openalex.org/W4366997336","doi":"https://doi.org/10.1145/3583131.3590356","title":"Calculating lexicase selection probabilities is NP-Hard","display_name":"Calculating lexicase selection probabilities is NP-Hard","publication_year":2023,"publication_date":"2023-07-12","ids":{"openalex":"https://openalex.org/W4366997336","doi":"https://doi.org/10.1145/3583131.3590356"},"language":"en","primary_location":{"id":"doi:10.1145/3583131.3590356","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3583131.3590356","pdf_url":null,"source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-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/A5039490105","display_name":"Emily Dolson","orcid":"https://orcid.org/0000-0001-8616-4898"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Emily Dolson","raw_affiliation_strings":["Michigan State University, East Lansing, United States of America"],"affiliations":[{"raw_affiliation_string":"Michigan State University, East Lansing, United States of America","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039490105"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":0.4526,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53517457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1575","last_page":"1583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9945999979972839,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9945999979972839,"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/T10521","display_name":"RNA and protein synthesis mechanisms","score":0.9606999754905701,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10878","display_name":"CRISPR and Genetic Engineering","score":0.9442999958992004,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.8633140921592712},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6233804225921631},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.49973011016845703},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48222076892852783},{"id":"https://openalex.org/keywords/selection-algorithm","display_name":"Selection algorithm","score":0.462799996137619},{"id":"https://openalex.org/keywords/brute-force","display_name":"Brute force","score":0.45512861013412476},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45203980803489685},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38884714245796204},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3247024118900299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31356099247932434},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24979615211486816}],"concepts":[{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.8633140921592712},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6233804225921631},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.49973011016845703},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48222076892852783},{"id":"https://openalex.org/C2775973920","wikidata":"https://www.wikidata.org/wiki/Q3252726","display_name":"Selection algorithm","level":3,"score":0.462799996137619},{"id":"https://openalex.org/C2986801135","wikidata":"https://www.wikidata.org/wiki/Q1209494","display_name":"Brute force","level":2,"score":0.45512861013412476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45203980803489685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38884714245796204},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3247024118900299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31356099247932434},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24979615211486816},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3583131.3590356","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3583131.3590356","pdf_url":null,"source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310016","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993"},{"id":"https://openalex.org/F4320332431","display_name":"College of Engineering, Michigan State University","ror":"https://ror.org/05hs6h993"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1978661986","https://openalex.org/W2034068348","https://openalex.org/W2036265926","https://openalex.org/W2401610261","https://openalex.org/W2484166844","https://openalex.org/W2798474464","https://openalex.org/W2830196635","https://openalex.org/W2882577511","https://openalex.org/W2898576908","https://openalex.org/W2912821124","https://openalex.org/W2921196120","https://openalex.org/W2961535796","https://openalex.org/W3023345483","https://openalex.org/W3046367554","https://openalex.org/W4284967583","https://openalex.org/W4289305969","https://openalex.org/W4289518271","https://openalex.org/W6912903030","https://openalex.org/W6969047179"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W4205762803","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W2535856026","https://openalex.org/W2354191502","https://openalex.org/W1788667622","https://openalex.org/W4317464041","https://openalex.org/W4366997336"],"abstract_inverted_index":{"Lexicase":[0],"selection":[1,6,84,145,148],"is":[2,93,127,185],"a":[3,43,102,119,161],"state-of-the-art":[4],"parent":[5],"algorithm":[7,164],"in":[8,108,117,194],"evolutionary":[9],"computation.":[10],"Recently,":[11],"there":[12],"have":[13,65],"been":[14],"efforts":[15,68],"to":[16,46,54,69,73,106,129],"develop":[17,70],"stronger":[18],"theoretical":[19,138],"analyses":[20],"of":[21,25,33,57,82,122,177,181,187,191],"lexicase":[22,40,60,74,87,123,131,147],"selection.":[23,41,75,132],"Many":[24],"these":[26,170],"analysis":[27],"hinge":[28],"on":[29],"calculating":[30,83],"the":[31,55,141,150,173,192],"probability":[32],"an":[34,114],"individual":[35],"solution":[36,179],"being":[37],"selected":[38],"under":[39,86],"Discovering":[42],"fast":[44],"way":[45],"perform":[47],"this":[48,80,97,178],"calculation":[49],"would":[50,63],"be":[51],"very":[52],"helpful":[53],"development":[56],"theory":[58],"regarding":[59],"selection,":[61,88,124,126],"and":[62,146,149,154],"also":[64,135],"implications":[66,139],"for":[67,168],"practical":[71],"improvements":[72],"Here,":[76],"I":[77,90,95,159],"prove":[78],"that":[79],"problem":[81,193],"probabilities":[85],"which":[89,118],"name":[91],"lex-prob,":[92],"NP-Hard.":[94],"achieve":[96],"proof":[98],"by":[99],"reducing":[100],"SAT,":[101],"well-known":[103],"NP-Hard":[104,156],"problem,":[105],"lex-prob":[107,153],"polynomial":[109],"time.":[110],"This":[111,133],"reduction":[112],"involves":[113],"intermediate":[115],"step":[116],"popular":[120],"variant":[121],"\u220a-lexicase":[125,144],"reduced":[128],"standard":[130],"result":[134],"has":[136],"deeper":[137],"about":[140],"relationship":[142,151],"between":[143,152],"other":[155],"problems.":[157],"Finally,":[158],"present":[160],"highly-optimized":[162],"brute-force":[163],"(and":[165],"open-source":[166],"implementation)":[167],"performing":[169],"calculations.":[171],"While":[172],"worst-case":[174],"time":[175],"complexity":[176],"is,":[180],"course,":[182],"exponential":[183],"it":[184],"capable":[186],"solving":[188],"realistically-sized":[189],"instances":[190],"approximately":[195],"15":[196],"seconds.":[197]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}