{"id":"https://openalex.org/W2032821770","doi":"https://doi.org/10.1561/0400000009","title":"Pairwise Independence and Derandomization","display_name":"Pairwise Independence and Derandomization","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2032821770","doi":"https://doi.org/10.1561/0400000009","mag":"2032821770"},"language":"en","primary_location":{"id":"doi:10.1561/0400000009","is_oa":false,"landing_page_url":"https://doi.org/10.1561/0400000009","pdf_url":null,"source":{"id":"https://openalex.org/S110848248","display_name":"Foundations and Trends\u00ae in Theoretical Computer Science","issn_l":"1551-305X","issn":["1551-305X","1551-3068"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Theoretical Computer Science","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/A5079654174","display_name":"Michael Luby","orcid":"https://orcid.org/0000-0002-6239-8072"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Luby","raw_affiliation_strings":["Digital Fountain, USA"],"affiliations":[{"raw_affiliation_string":"Digital Fountain, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":["Institute for Advanced Study, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study, USA","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079654174"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.0598,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.97043011,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"1","issue":"4","first_page":"237","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9970999956130981,"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/pairwise-independence","display_name":"Pairwise independence","score":0.8512553572654724},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.7473925948143005},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.6655789017677307},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6404623985290527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5533235669136047},{"id":"https://openalex.org/keywords/sum-of-normally-distributed-random-variables","display_name":"Sum of normally distributed random variables","score":0.49460265040397644},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.49003565311431885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4547249376773834},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4498459994792938},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.4289109408855438},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42412033677101135},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.41438359022140503},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.37714967131614685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37665069103240967}],"concepts":[{"id":"https://openalex.org/C114928208","wikidata":"https://www.wikidata.org/wiki/Q17104952","display_name":"Pairwise independence","level":5,"score":0.8512553572654724},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.7473925948143005},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6655789017677307},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6404623985290527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5533235669136047},{"id":"https://openalex.org/C182514268","wikidata":"https://www.wikidata.org/wiki/Q7636889","display_name":"Sum of normally distributed random variables","level":4,"score":0.49460265040397644},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.49003565311431885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4547249376773834},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4498459994792938},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.4289109408855438},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42412033677101135},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.41438359022140503},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37714967131614685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37665069103240967},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1561/0400000009","is_oa":false,"landing_page_url":"https://doi.org/10.1561/0400000009","pdf_url":null,"source":{"id":"https://openalex.org/S110848248","display_name":"Foundations and Trends\u00ae in Theoretical Computer Science","issn_l":"1551-305X","issn":["1551-305X","1551-3068"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:berkeley.edu:13030-hb3r29p10g","is_oa":false,"landing_page_url":"http://techreports.lib.berkeley.edu/accessPages/CSD-95-880.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407050879","display_name":"UC Berkeley","issn_l":null,"issn":[],"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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"technical reports"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.126.8552","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.8552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ias.edu/~avi/BOOKS/TCS003-1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.6485","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.6485","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ias.edu/~avi/PUBLICATIONS/Pairwise_Independence_and_Derandomization.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.7253","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7253","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dimacs.rutgers.edu/~dieter/Seminar/Papers/lw-PWindependence.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.406.4799","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.4799","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/Pubs/TechRpts/1995/CSD-95-880.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.8687","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.8687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.icsi.berkeley.edu/pub/techreports/1995/tr-95-035.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.2375","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.2375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wisc.edu/~jyc/luby-wigderson.ps","raw_type":"text"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-032633526","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1964089073","https://openalex.org/W1976907131","https://openalex.org/W1984976620","https://openalex.org/W1985623009","https://openalex.org/W1992626439","https://openalex.org/W1994584977","https://openalex.org/W1998400388","https://openalex.org/W1998918799","https://openalex.org/W2006912660","https://openalex.org/W2007746582","https://openalex.org/W2014850486","https://openalex.org/W2015880590","https://openalex.org/W2017290750","https://openalex.org/W2018047324","https://openalex.org/W2019038806","https://openalex.org/W2023915883","https://openalex.org/W2027528470","https://openalex.org/W2036656440","https://openalex.org/W2045924252","https://openalex.org/W2049182037","https://openalex.org/W2055756054","https://openalex.org/W2057512592","https://openalex.org/W2061106457","https://openalex.org/W2062767125","https://openalex.org/W2064423787","https://openalex.org/W2069919161","https://openalex.org/W2094500233","https://openalex.org/W2100061495","https://openalex.org/W2107324709","https://openalex.org/W2108104892","https://openalex.org/W2110824700","https://openalex.org/W2117362057","https://openalex.org/W2126274204","https://openalex.org/W2131798840","https://openalex.org/W2134490689","https://openalex.org/W2155506366","https://openalex.org/W2164284862","https://openalex.org/W2165621523","https://openalex.org/W2281668463","https://openalex.org/W2293097972","https://openalex.org/W2969734899"],"related_works":["https://openalex.org/W2117280242","https://openalex.org/W2389562836","https://openalex.org/W4307700710","https://openalex.org/W2083019828","https://openalex.org/W3214736939","https://openalex.org/W4385568595","https://openalex.org/W4245457074","https://openalex.org/W2389432337","https://openalex.org/W2027272923","https://openalex.org/W4239221418"],"abstract_inverted_index":{"This":[0],"article":[1,93],"gives":[2],"several":[3],"applications":[4],"of":[5,35,86,99,119,134,169,204],"the":[6,32,36,42,47,53,84,103,108,113,128,132,135,142,159,167,194,205,220,234],"following":[7,235],"paradigm,":[8],"which":[9],"has":[10,164],"proven":[11,71],"extremely":[12],"powerful":[13],"in":[14,77,105,127,166,223],"algorithm":[15,24,37,48],"design":[16,21],"and":[17,76,121,171,174,182,200,226,237],"computational":[18,81,230],"complexity.":[19],"First,":[20],"a":[22,26,59,97,145,156,176,202],"probabilistic":[23],"for":[25],"given":[27,101,191],"problem.":[28],"Then,":[29],"show":[30],"that":[31,151],"correctness":[33],"analysis":[34],"remains":[38],"valid":[39],"even":[40],"when":[41],"random":[43],"strings":[44],"used":[45],"by":[46,102,112],"do":[49],"not":[50],"come":[51],"from":[52,58],"uniform":[54],"distribution,":[55],"but":[56],"rather":[57],"small":[60],"sample":[61],"space,":[62],"appropriately":[63],"chosen.":[64],"In":[65],"some":[66],"cases":[67],"this":[68,152],"can":[69,124],"be":[70,125,186],"directly":[72],"(giving":[73,89],"\u201cunconditional":[74],"derandomization\u201d),":[75],"others":[78],"it":[79],"uses":[80],"assumptions,":[82],"like":[83],"existence":[85],"1-way":[87],"functions":[88],"\u201cconditional":[90],"derandomization\u201d).":[91],"The":[92,137,209],"is":[94,140,197,201],"based":[95],"on":[96],"series":[98],"lectures":[100,160,190],"authors":[104],"1995,":[106],"where":[107],"notes":[109],"were":[110,161,188],"scribed":[111],"attending":[114],"students.":[115],"(The":[116],"detailed":[117],"list":[118],"scribes":[120],"other":[122],"contributors":[123],"found":[126],"Acknowledgements":[129],"section":[130],"at":[131],"end":[133],"manuscript.)":[136],"current":[138],"version":[139],"essentially":[141],"same,":[143],"with":[144,229],"few":[146],"minor":[147],"changes.":[148],"We":[149,218],"note":[150],"publication":[153],"takes":[154],"place":[155],"decade":[157],"after":[158],"given.":[162],"Much":[163],"happened":[165],"area":[168],"pseudorandomness":[170],"derandomization":[172,225],"since,":[173],"perhaps":[175],"somewhat":[177],"different":[178,180,183],"viewpoint,":[179],"material,":[181],"style":[184],"would":[185],"chosen":[187],"these":[189],"today.":[192],"Still,":[193],"material":[195,210],"presented":[196],"self":[198],"contained,":[199],"primemanifestation":[203],"\u201cderandomization":[206],"\u201d":[207],"paradigm.":[208],"does":[211],"lack":[212],"references":[213],"to":[214,232],"newer":[215],"work":[216],"though.":[217],"recommend":[219],"reader":[221],"interested":[222],"randomness,":[224],"their":[227],"interplay":[228],"complexity":[231],"consult":[233],"books":[236],"surveys,":[238],"as":[239],"well":[240]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
