{"id":"https://openalex.org/W1977055509","doi":"https://doi.org/10.1109/tcad.2008.2009143","title":"Non-Gaussian Statistical Timing Analysis Using Second-Order Polynomial Fitting","display_name":"Non-Gaussian Statistical Timing Analysis Using Second-Order Polynomial Fitting","publication_year":2008,"publication_date":"2008-12-22","ids":{"openalex":"https://openalex.org/W1977055509","doi":"https://doi.org/10.1109/tcad.2008.2009143","mag":"1977055509"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2008.2009143","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2008.2009143","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","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/A5104049811","display_name":"Lerong Cheng","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":"Lerong Cheng","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","Dept. of Electr. Eng., Univ. of California at Los Angeles, Los Angeles, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of California at Los Angeles, Los Angeles, CA#TAB#","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"]},{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jinjun Xiong","raw_affiliation_strings":["IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA","IBM Thomas J. Watson Research Center Yorktown Heights, NY#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I4210114115"]},{"raw_affiliation_string":"IBM Thomas J. Watson Research Center Yorktown Heights, NY#TAB#","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008695429","display_name":"Lei He","orcid":"https://orcid.org/0000-0002-5266-3805"},"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":"Lei He","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","Dept. of Electr. Eng., Univ. of California at Los Angeles, Los Angeles, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of California at Los Angeles, Los Angeles, CA#TAB#","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3664,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.93970254,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"1","first_page":"130","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","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 high-performance VLSI design","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":"VLSI and Analog Circuit Testing","score":0.9998999834060669,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9997000098228455,"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/skewness","display_name":"Skewness","score":0.7189845442771912},{"id":"https://openalex.org/keywords/standard-deviation","display_name":"Standard deviation","score":0.633345365524292},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5936184525489807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5911111831665039},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4898955225944519},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4881230294704437},{"id":"https://openalex.org/keywords/polynomial-and-rational-function-modeling","display_name":"Polynomial and rational function modeling","score":0.4806429445743561},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4518702030181885},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4518432915210724},{"id":"https://openalex.org/keywords/kurtosis","display_name":"Kurtosis","score":0.43409299850463867},{"id":"https://openalex.org/keywords/percentile","display_name":"Percentile","score":0.4336521327495575},{"id":"https://openalex.org/keywords/process-variation","display_name":"Process variation","score":0.4105485677719116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34412074089050293},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3364349603652954},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.1838218867778778},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09340369701385498}],"concepts":[{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.7189845442771912},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.633345365524292},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5936184525489807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5911111831665039},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4898955225944519},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4881230294704437},{"id":"https://openalex.org/C138029060","wikidata":"https://www.wikidata.org/wiki/Q7226633","display_name":"Polynomial and rational function modeling","level":3,"score":0.4806429445743561},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4518702030181885},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4518432915210724},{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.43409299850463867},{"id":"https://openalex.org/C122048520","wikidata":"https://www.wikidata.org/wiki/Q2913954","display_name":"Percentile","level":2,"score":0.4336521327495575},{"id":"https://openalex.org/C93389723","wikidata":"https://www.wikidata.org/wiki/Q7247313","display_name":"Process variation","level":3,"score":0.4105485677719116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34412074089050293},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3364349603652954},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.1838218867778778},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09340369701385498},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcad.2008.2009143","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2008.2009143","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.579.4968","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.579.4968","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cecs.uci.edu/~papers/aspdac08/pdf/p298_4A-3.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3837248487","display_name":"CAREER: Interconnect-Centric Layout Synthesis and Planning with Consideration of On-Chip Inductance","funder_award_id":"0401682","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G490777091","display_name":"CAREER: Interconnect-Centric Layout Synthesis and Planning with Consideration of On-Chip Inductance","funder_award_id":"0093273","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1498699371","https://openalex.org/W1966741973","https://openalex.org/W1999520218","https://openalex.org/W2002591317","https://openalex.org/W2006447899","https://openalex.org/W2045851496","https://openalex.org/W2065183790","https://openalex.org/W2074952123","https://openalex.org/W2103323734","https://openalex.org/W2104785869","https://openalex.org/W2106461028","https://openalex.org/W2106753198","https://openalex.org/W2112662324","https://openalex.org/W2117648153","https://openalex.org/W2121437951","https://openalex.org/W2123021960","https://openalex.org/W2126564504","https://openalex.org/W2132844001","https://openalex.org/W2141222031","https://openalex.org/W2142213725","https://openalex.org/W2147120839","https://openalex.org/W2160202300","https://openalex.org/W2163262735","https://openalex.org/W2165740397","https://openalex.org/W2166751677","https://openalex.org/W2169132964","https://openalex.org/W4230540414","https://openalex.org/W4230672423","https://openalex.org/W4233806716","https://openalex.org/W4237955880","https://openalex.org/W4243549705","https://openalex.org/W4245502288","https://openalex.org/W4246743157","https://openalex.org/W6641884055","https://openalex.org/W6675376406","https://openalex.org/W6683774987"],"related_works":["https://openalex.org/W4225568567","https://openalex.org/W1496883226","https://openalex.org/W4297337052","https://openalex.org/W2028605949","https://openalex.org/W4286378979","https://openalex.org/W2282665605","https://openalex.org/W3216026256","https://openalex.org/W3129919015","https://openalex.org/W4390742338","https://openalex.org/W2041010645"],"abstract_inverted_index":{"For":[0],"nanometer":[1],"manufacturing,":[2],"process":[3,25],"variation":[4,37,45],"causes":[5],"significant":[6],"uncertainty":[7],"for":[8,81,116],"circuit":[9],"performance":[10],"verification.":[11],"Statistical":[12],"static":[13],"timing":[14,22],"analysis":[15],"(SSTA)":[16],"is":[17],"thus":[18],"developed":[19],"to":[20,57,124],"estimate":[21],"distribution":[23,38],"under":[24],"variation.":[26],"Most":[27],"existing":[28],"SSTA":[29,79],"techniques":[30],"have":[31],"difficulty":[32],"in":[33],"handling":[34],"the":[35,59,98,125,132],"non-Gaussian":[36,64,78],"and":[39,94,102,137,145],"nonlinear":[40],"dependence":[41],"of":[42,62,104],"delay":[43,83],"on":[44],"sources.":[46],"To":[47],"address":[48],"this":[49],"problem,":[50],"we":[51,74],"first":[52],"propose":[53],"a":[54],"new":[55,77],"method":[56],"approximate":[58],"max":[60],"operation":[61],"two":[63],"random":[65],"variables":[66],"through":[67],"second-order":[68],"polynomial":[69],"fitting.":[70],"With":[71],"such":[72],"approximation,":[73],"then":[75],"present":[76],"algorithms":[80,106],"three":[82],"models:":[84],"quadratic":[85,87],"model,":[86],"model":[88],"without":[89],"crossing":[90],"terms":[91],"(semiquadratic":[92],"model),":[93],"linear":[95],"model.":[96],"All":[97],"atomic":[99],"operations":[100],"(max":[101],"sum)":[103],"our":[105,129],"are":[107],"performed":[108],"by":[109],"closed-form":[110],"formulas;":[111],"hence,":[112],"they":[113],"scale":[114],"well":[115],"large":[117],"designs.":[118],"Experimental":[119],"results":[120],"show":[121],"that":[122],"compared":[123],"Monte":[126],"Carlo":[127],"simulation,":[128],"approach":[130],"predicts":[131],"mean,":[133],"standard":[134],"deviation,":[135],"skewness,":[136],"95%":[138],"percentile":[139],"point":[140],"within":[141],"1%,":[142,143],"6%,":[144],"1%":[146],"error,":[147],"respectively.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
