{"id":"https://openalex.org/W2972401921","doi":"https://doi.org/10.1145/3349613","title":"PPSZ for <i>k</i> \u2265 5: More Is Better","display_name":"PPSZ for <i>k</i> \u2265 5: More Is Better","publication_year":2019,"publication_date":"2019-09-12","ids":{"openalex":"https://openalex.org/W2972401921","doi":"https://doi.org/10.1145/3349613","mag":"2972401921"},"language":"en","primary_location":{"id":"doi:10.1145/3349613","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3349613","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","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/A5034846265","display_name":"Dominik Scheder","orcid":"https://orcid.org/0000-0002-9360-7957"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dominik Scheder","raw_affiliation_strings":["Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034846265"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14338617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"4","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T11567","display_name":"semigroups and automata theory","score":0.9973999857902527,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/combinatorics","display_name":"Combinatorics","score":0.8300907015800476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.790866494178772},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5794168710708618},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5190118551254272},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49212855100631714},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4838792085647583},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.4607689380645752},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.4414644241333008},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4304538369178772},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08203789591789246}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8300907015800476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.790866494178772},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5794168710708618},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5190118551254272},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49212855100631714},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4838792085647583},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.4607689380645752},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4414644241333008},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4304538369178772},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08203789591789246},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3349613","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3349613","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2911442015","display_name":null,"funder_award_id":"61502300","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W97263645","https://openalex.org/W282603215","https://openalex.org/W1479933940","https://openalex.org/W1587069206","https://openalex.org/W1971361630","https://openalex.org/W2020913456","https://openalex.org/W2049136377","https://openalex.org/W2092928619","https://openalex.org/W2119274015","https://openalex.org/W2120698547","https://openalex.org/W2126442135","https://openalex.org/W2404429313","https://openalex.org/W2753431681","https://openalex.org/W2952109563","https://openalex.org/W2963722463","https://openalex.org/W4206871748"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2949964783","https://openalex.org/W2768610039","https://openalex.org/W3121250382","https://openalex.org/W4285390085","https://openalex.org/W31688704","https://openalex.org/W2801357573","https://openalex.org/W2974000959","https://openalex.org/W2097752597"],"abstract_inverted_index":{"We":[0,189,201],"show":[1,28,202],"that":[2,29,51,153,194,234],"for":[3,10,30,119,183],"k":[4,11,32,60,86,102,120],"\u2265":[5,33],"5,":[6,34],"the":[7,53,110,208,256],"PPSZ":[8,74],"algorithm":[9],"-SAT":[12],"runs":[13],"exponentially":[14],"faster":[15],"if":[16,225],"there":[17,35],"is":[18,36,58,109,223,227],"an":[19,252],"exponential":[20,239,253],"number":[21],"of":[22,161,198,238,244,255,259],"satisfying":[23,77,126],"assignments.":[24],"More":[25],"precisely,":[26],"we":[27,144],"every":[31,235],"a":[37,59,76,124,132,136,165,169,196,205,228,242],"strictly":[38],"increasing":[39],"function":[40],"f":[41,47,94],":":[42,213],"[0,1]":[43],"\u2192":[44],"R":[45],"with":[46,79,123],"(0)":[48],"=":[49,68,178,215],"0":[50],"has":[52],"following":[54],"property.":[55],"If":[56],"F":[57],"-CNF":[61,121],"formula":[62],"over":[63],"n":[64,71,87,91,96,103,107,142,149,182],"variables":[65],"and":[66],"|sat(F)|":[67],"2":[69,83,99,181],"\u03b4":[70],"solutions,":[72],"then":[73],"finds":[75],"assignment":[78],"probability":[80,112,258],"at":[81],"least":[82],"\u2212":[84,88,100,104],"c":[85,101],"o":[89,105],"(":[90,106,220],")":[92,108],"+":[93],"(\u03b4)":[95],".":[97,163,188],"Here,":[98],"success":[111,257],"proved":[113],"by":[114],"Paturi":[115],"et":[116],"al.":[117],"[11]":[118],"formulas":[122],"unique":[125],"assignment.":[127],"Our":[128],"proof":[129],"rests":[130],"on":[131,171],"combinatorial":[133],"lemma:":[134],"given":[135],"set":[137,236],"S":[138,162,212,226,237],"\u2286":[139],"{":[140,147],"0,1}":[141,148],",":[143],"can":[145],"partition":[146,166,243],"into":[150],"subcubes":[151],"such":[152],"each":[154,184],"subcube":[155],"B":[156,167,176,185,187,218,221],"contains":[157],"exactly":[158],"one":[159],"element":[160],"Such":[164],"induces":[168],"distribution":[170,197],"itself,":[172],"via":[173],"Pr":[174],"[":[175],"]":[177],"|B|":[179],"/":[180],"\u2208":[186],"are":[190],"interested":[191],"in":[192,204,248],"partitions":[193],"induce":[195],"high":[199],"entropy.":[200,246],"that,":[203],"certain":[206],"sense,":[207],"worst":[209],"case":[210],"(min":[211],"|S|":[214],"s":[216],"max":[217],"H":[219],"))":[222],"achieved":[224],"Hamming":[229],"ball.":[230],"This":[231,247],"lemma":[232],"implies":[233],"size":[240],"allows":[241],"linear":[245],"turn":[249],"leads":[250],"to":[251],"improvement":[254],"PPSZ.":[260]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
