{"id":"https://openalex.org/W1985250014","doi":"https://doi.org/10.1002/rsa.3240070105","title":"Tail bounds for occupancy and the satisfiability threshold conjecture","display_name":"Tail bounds for occupancy and the satisfiability threshold conjecture","publication_year":1995,"publication_date":"1995-08-01","ids":{"openalex":"https://openalex.org/W1985250014","doi":"https://doi.org/10.1002/rsa.3240070105","mag":"1985250014"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240070105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240070105","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","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/A5011557822","display_name":"Anil Kamath","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anil Kamath","raw_affiliation_strings":["Department of Computer Science, Stanford University, Stanford, CA 94305\u20132140","Department of Computer Science, Stanford University, Stanford, CA 94305-2140"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA 94305\u20132140","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA 94305-2140","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112649653","display_name":"Rajeev Motwani","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rajeev Motwani","raw_affiliation_strings":["Department of Computer Science, Stanford University, Stanford, CA 94305\u20132140","Department of Computer Science, Stanford University, Stanford, CA 94305-2140"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA 94305\u20132140","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA 94305-2140","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061421817","display_name":"Krishna V. Palem","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Krishna Palem","raw_affiliation_strings":["Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY 10012","Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY 10012#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY 10012","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Department of Computer Science, Courant Institute of Mathematical Sciences, New York, NY 10012#TAB#","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011756177","display_name":"Paul G. Spirakis","orcid":"https://orcid.org/0000-0001-5396-3749"},"institutions":[{"id":"https://openalex.org/I120729142","display_name":"Research Academic Computer Technology Institute","ror":"https://ror.org/021nszj63","country_code":"GR","type":"facility","lineage":["https://openalex.org/I120729142","https://openalex.org/I4210154149"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Paul Spirakis","raw_affiliation_strings":["Computer Technology institute, Patras University, Greece","Computer Technology Institute, Patras University, Greece"],"affiliations":[{"raw_affiliation_string":"Computer Technology institute, Patras University, Greece","institution_ids":["https://openalex.org/I120729142"]},{"raw_affiliation_string":"Computer Technology Institute, Patras University, Greece","institution_ids":["https://openalex.org/I120729142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011557822"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":8.58050777,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.98258598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"1","first_page":"59","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9923999905586243,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9923999905586243,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9872999787330627,"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/T11567","display_name":"semigroups and automata theory","score":0.9817000031471252,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.875088095664978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7337325215339661},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7273806929588318},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6907322406768799},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5416155457496643},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5318063497543335},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47997522354125977},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.45901811122894287},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4352588653564453},{"id":"https://openalex.org/keywords/occupancy","display_name":"Occupancy","score":0.4233148396015167},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.41966676712036133},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4102640151977539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13560962677001953},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13154655694961548},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.055820316076278687}],"concepts":[{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.875088095664978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7337325215339661},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7273806929588318},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6907322406768799},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5416155457496643},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5318063497543335},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47997522354125977},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.45901811122894287},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4352588653564453},{"id":"https://openalex.org/C160331591","wikidata":"https://www.wikidata.org/wiki/Q7075743","display_name":"Occupancy","level":2,"score":0.4233148396015167},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.41966676712036133},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4102640151977539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13560962677001953},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13154655694961548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.055820316076278687},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/rsa.3240070105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240070105","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W17078302","https://openalex.org/W1963913579","https://openalex.org/W1969966778","https://openalex.org/W1973240854","https://openalex.org/W1999678910","https://openalex.org/W2002651865","https://openalex.org/W2018251959","https://openalex.org/W2022695609","https://openalex.org/W2054387247","https://openalex.org/W2068871408","https://openalex.org/W2091968492","https://openalex.org/W2099546535","https://openalex.org/W2126420408","https://openalex.org/W2164346692","https://openalex.org/W2912284828","https://openalex.org/W4231916799"],"related_works":["https://openalex.org/W4282043467","https://openalex.org/W2105697914","https://openalex.org/W3093197249","https://openalex.org/W1540010871","https://openalex.org/W3023979140","https://openalex.org/W1968324288","https://openalex.org/W2904068067","https://openalex.org/W1565491139","https://openalex.org/W2041927040","https://openalex.org/W2526609438"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"classical":[2],"occupancy":[3,158],"problem":[4],"is":[5,56,81,101,134,141],"concerned":[6],"with":[7,72,136],"studying":[8],"the":[9,33,36,57,65,87,119,157],"number":[10,37],"of":[11,19,29,35,38,89,92,121,148,156],"empty":[12,39],"bins":[13],"resulting":[14],"from":[15,86],"a":[16,27,102,114,130,144],"random":[17,69,131],"allocation":[18],"m":[20],"balls":[21],"to":[22],"n":[23,76],"bins.":[24,40],"We":[25,112],"provide":[26,113],"series":[28],"tail":[30,42,159],"bounds":[31,43],"on":[32,61,118,143],"distribution":[34],"These":[41],"should":[44],"find":[45],"application":[46,55],"in":[47],"randomized":[48],"algorithms":[49],"and":[50,84],"probabilistic":[51],"analysis.":[52],"Our":[53],"motivating":[54],"following":[58],"well\u2010known":[59],"conjecture":[60],"threshold":[62,104],"phenomenon":[63],"for":[64,105,126],"satisfiability":[66,106],"problem.":[67],"Consider":[68],"3\u2010SAT":[70,132],"formulas":[71],"cn":[73],"clauses":[74,91],"over":[75],"variables,":[77],"where":[78],"each":[79],"clause":[80],"chosen":[82],"uniformly":[83],"independently":[85],"space":[88],"all":[90],"size":[93],"3.":[94],"It":[95],"has":[96],"been":[97],"conjectured":[98],"that":[99,125],"there":[100],"sharp":[103],"at":[107],"c":[108,122,127],"*":[109],"\u2248\ufe01":[110],"4.2.":[111],"strong":[115],"upper":[116],"bound":[117],"value":[120],"*,":[123],"showing":[124],">":[128],"4.758":[129],"formula":[133],"unsatisfiable":[135],"high":[137],"probability.":[138],"This":[139],"result":[140],"based":[142],"structural":[145],"property,":[146],"possibly":[147],"independent":[149],"interest,":[150],"whose":[151],"proof":[152],"needs":[153],"several":[154],"applications":[155],"bounds.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}