{"id":"https://openalex.org/W2040272297","doi":"https://doi.org/10.1109/tvlsi.2011.2157843","title":"Fourier Series Approximation for Max Operation in Non-Gaussian and Quadratic Statistical Static Timing Analysis","display_name":"Fourier Series Approximation for Max Operation in Non-Gaussian and Quadratic Statistical Static Timing Analysis","publication_year":2011,"publication_date":"2011-07-06","ids":{"openalex":"https://openalex.org/W2040272297","doi":"https://doi.org/10.1109/tvlsi.2011.2157843","mag":"2040272297"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2011.2157843","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://eda.ee.ucla.edu/pub/J71.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104049811","display_name":"Lerong Cheng","orcid":null},"institutions":[],"countries":["US"],"is_corresponding":false,"raw_author_name":"None Lerong Cheng","raw_affiliation_strings":["SanDisk Corporation, Milpitas, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"SanDisk Corporation, Milpitas, CA, USA#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111918002","display_name":"Fang Gong","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"None Fang Gong","raw_affiliation_strings":["Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035679293","display_name":"Wenyao Xu","orcid":"https://orcid.org/0000-0001-6444-9411"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"None Wenyao Xu","raw_affiliation_strings":["Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030156276","display_name":"Jinjun Xiong","orcid":"https://orcid.org/0000-0002-2620-4859"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"None Jinjun Xiong","raw_affiliation_strings":["[IBM Thomas J. Watson Research Center, Yorktown Heights, NY , USA]"],"affiliations":[{"raw_affiliation_string":"[IBM Thomas J. Watson Research Center, Yorktown Heights, NY , USA]","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100317858","display_name":"Lei He","orcid":"https://orcid.org/0000-0002-3821-2047"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"None Lei He","raw_affiliation_strings":["Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Dept., of Electr. Eng., Univ. of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078132977","display_name":"Majid Sarrafzadeh","orcid":"https://orcid.org/0000-0001-8407-8689"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Sarrafzadeh","raw_affiliation_strings":["Department of Computer Science, University of California, Los Angeles , CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Los Angeles , CA, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.076,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":12,"citation_normalized_percentile":{"value":0.781468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":86,"max":87},"biblio":{"volume":"20","issue":"8","first_page":"1383","last_page":"1391"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-Power VLSI Circuit Design and Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10363","display_name":"Low-Power VLSI Circuit Design and Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11032","display_name":"Very Large Scale Integration Testing","score":0.9999,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10472","display_name":"Atomic Layer Deposition Technology","score":0.9998,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-timing-analysis","display_name":"Statistical Timing Analysis","score":0.576735},{"id":"https://openalex.org/keywords/delay-fault-testing","display_name":"Delay Fault Testing","score":0.518415}],"concepts":[{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.6621537},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.66015136},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6468971},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.5497367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48219815},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4256281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39560542},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34625632},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1831465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2011.2157843","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.707.2578","pdf_url":"http://eda.ee.ucla.edu/pub/J71.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.707.2578","pdf_url":"http://eda.ee.ucla.edu/pub/J71.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":30,"referenced_works":["https://openalex.org/W1498699371","https://openalex.org/W1973615069","https://openalex.org/W1977055509","https://openalex.org/W1999520218","https://openalex.org/W2002591317","https://openalex.org/W2006447899","https://openalex.org/W2065183790","https://openalex.org/W2099894450","https://openalex.org/W2101264278","https://openalex.org/W2103323734","https://openalex.org/W2104785869","https://openalex.org/W2112662324","https://openalex.org/W2121437951","https://openalex.org/W2126564504","https://openalex.org/W2129930123","https://openalex.org/W2130195423","https://openalex.org/W2132844001","https://openalex.org/W2141222031","https://openalex.org/W2142213725","https://openalex.org/W2149342513","https://openalex.org/W2157210245","https://openalex.org/W2163262735","https://openalex.org/W2163444751","https://openalex.org/W2163626738","https://openalex.org/W2165740397","https://openalex.org/W4236674018","https://openalex.org/W4237771567","https://openalex.org/W4245502288","https://openalex.org/W4246743157","https://openalex.org/W4253856301"],"related_works":["https://openalex.org/W3144675622","https://openalex.org/W3124374489","https://openalex.org/W3122032734","https://openalex.org/W28389960","https://openalex.org/W2771883571","https://openalex.org/W2189529952","https://openalex.org/W2163571608","https://openalex.org/W2153442034","https://openalex.org/W2084723156","https://openalex.org/W1993982689"],"abstract_inverted_index":{"The":[0],"most":[1,117],"challenging":[2],"problem":[3],"in":[4,70,131],"the":[5,17,67,100,124,162,176],"current":[6],"block-based":[7],"statistical":[8],"static":[9],"timing":[10],"analysis":[11],"(SSTA)":[12],"is":[13,129],"how":[14],"to":[15,45,49,65,147],"handle":[16,50,66],"max":[18,68,103],"operation":[19,69],"efficiently":[20,108],"and":[21,77,95,104,135,155,166,175],"accurately.":[22],"Existing":[23],"SSTA":[24,71,89],"techniques":[25],"suffer":[26],"from":[27],"limited":[28],"modeling":[29],"capability":[30],"by":[31],"using":[32],"a":[33],"linear":[34,130],"delay":[35,75,93,157],"model":[36,94],"with":[37,72,91,170,178],"Gaussian":[38],"distribution,":[39],"or":[40,54,113],"have":[41],"scalability":[42],"problems":[43],"due":[44],"expensive":[46],"operations":[47],"involved":[48],"non-Gaussian":[51,78,96,152],"variation":[52,79,97,133,153],"sources":[53,80,134,154],"nonlinear":[55,156],"delays.":[56],"To":[57],"overcome":[58],"these":[59],"limitations,":[60],"we":[61,86],"propose":[62],"efficient":[63],"algorithms":[64],"both":[73,132],"quadratic":[74,92],"dependency":[76],"simultaneously.":[81],"Based":[82],"on":[83],"such":[84],"algorithms,":[85],"develop":[87],"an":[88],"flow":[90],"sources.":[98],"All":[99],"atomic":[101],"operations,":[102],"add,":[105],"are":[106],"calculated":[107],"via":[109],"either":[110],"closed-form":[111],"formulas":[112],"low":[114],"dimension":[115],"(at":[116],"2-D)":[118],"lookup":[119],"tables.":[120],"We":[121],"prove":[122],"that":[123],"complexity":[125],"of":[126],"our":[127,139,159],"algorithm":[128,140],"circuit":[136],"sizes,":[137],"hence":[138],"scales":[141],"well":[142],"for":[143,151],"large":[144],"designs.":[145],"Compared":[146],"Monte":[148],"Carlo":[149],"simulation":[150],"models,":[158],"approach":[160],"predicts":[161],"mean,":[163],"standard":[164],"deviation":[165],"95%":[167],"percentile":[168],"point":[169],"less":[171,179],"than":[172,180],"2%":[173],"error,":[174],"skewness":[177],"10%":[181],"error.":[182]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2040272297","counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2024-11-21T05:00:18.967047","created_date":"2016-06-24"}