{"id":"https://openalex.org/W2136092716","doi":"https://doi.org/10.1109/isqed.2008.4479699","title":"Adaptive Stochastic Collocation Method (ASCM) for Parameterized Statistical Timing Analysis with Quadratic Delay Model","display_name":"Adaptive Stochastic Collocation Method (ASCM) for Parameterized Statistical Timing Analysis with Quadratic Delay Model","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2136092716","doi":"https://doi.org/10.1109/isqed.2008.4479699","mag":"2136092716"},"language":"en","primary_location":{"id":"doi:10.1109/isqed.2008.4479699","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isqed.2008.4479699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"9th International Symposium on Quality Electronic Design (isqed 2008)","raw_type":"proceedings-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/A5100764493","display_name":"Yi Wang","orcid":"https://orcid.org/0000-0001-8042-5970"},"institutions":[{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yi Wang","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064213921","display_name":"Xuan Zeng","orcid":"https://orcid.org/0000-0002-8097-4053"},"institutions":[{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Zeng","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062927280","display_name":"Jun Tao","orcid":"https://orcid.org/0000-0001-8742-687X"},"institutions":[{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Tao","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020841047","display_name":"Hengliang Zhu","orcid":"https://orcid.org/0000-0002-0338-9256"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hengliang Zhu","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102873970","display_name":"Xu Luo","orcid":"https://orcid.org/0000-0001-6942-896X"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Luo","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037328458","display_name":"Changhao Yan","orcid":"https://orcid.org/0000-0002-8936-3945"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I4391767673","display_name":"State Key Laboratory of ASIC and System","ror":"https://ror.org/01mamgv83","country_code":null,"type":"facility","lineage":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changhao Yan","raw_affiliation_strings":["Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","*Fudan University, Shanghai"],"affiliations":[{"raw_affiliation_string":"Microelectronics Department State Key Laboratory of ASIC & SystemFudan, University of Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"]},{"raw_affiliation_string":"*Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044102523","display_name":"Wei Cai","orcid":"https://orcid.org/0000-0002-7622-4532"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Cai","raw_affiliation_strings":["Department of Mathematics, University of North Carolina, Charlotte, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of North Carolina, Charlotte, USA","institution_ids":["https://openalex.org/I102149020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5100764493"],"corresponding_institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4391767673"],"apc_list":null,"apc_paid":null,"fwci":1.9168,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87865546,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":null,"first_page":"62","last_page":"67"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","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"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9986000061035156,"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/collocation","display_name":"Collocation (remote sensing)","score":0.6120730638504028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5542529821395874},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.5481744408607483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5366157293319702},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4931895136833191},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.4746097922325134},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4554961323738098},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.45376861095428467},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4457446336746216},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4445398151874542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3598809242248535}],"concepts":[{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6120730638504028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5542529821395874},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.5481744408607483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5366157293319702},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4931895136833191},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.4746097922325134},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4554961323738098},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.45376861095428467},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4457446336746216},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4445398151874542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3598809242248535},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isqed.2008.4479699","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isqed.2008.4479699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"9th International Symposium on Quality Electronic Design (isqed 2008)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1667165204","https://openalex.org/W1999520218","https://openalex.org/W2018159038","https://openalex.org/W2020328455","https://openalex.org/W2036488048","https://openalex.org/W2065183790","https://openalex.org/W2103455761","https://openalex.org/W2105302023","https://openalex.org/W2112662324","https://openalex.org/W2132844001","https://openalex.org/W2141222031","https://openalex.org/W2142213725","https://openalex.org/W2143591652","https://openalex.org/W2158750015","https://openalex.org/W2158812231","https://openalex.org/W2161288243","https://openalex.org/W2163262735","https://openalex.org/W2165740397","https://openalex.org/W4233806716","https://openalex.org/W4246458327","https://openalex.org/W4246743157","https://openalex.org/W4250849991","https://openalex.org/W6641884055"],"related_works":["https://openalex.org/W2125712855","https://openalex.org/W2031073114","https://openalex.org/W2884941144","https://openalex.org/W1989122168","https://openalex.org/W2994527389","https://openalex.org/W2908969745","https://openalex.org/W3128387452","https://openalex.org/W2044631309","https://openalex.org/W2019357411","https://openalex.org/W70375917"],"abstract_inverted_index":{"In":[0,41],"this":[1],"paper,":[2],"we":[3],"propose":[4],"an":[5],"adaptive":[6,19],"stochastic":[7,70,82],"collocation":[8,71,83],"method":[9,20,60,101,147],"for":[10],"block-based":[11],"statistical":[12],"static":[13],"timing":[14,56],"analysis":[15],"(SSTA).":[16],"A":[17],"novel":[18],"is":[21],"proposed":[22,59,100,117,146],"to":[23,43],"perform":[24],"SSTA":[25],"with":[26,79,126,132],"delays":[27],"of":[28,69,113,144],"gates":[29],"and":[30,92,156,158],"interconnects":[31],"modeled":[32],"by":[33,73],"quadratic":[34],"polynomials":[35],"based":[36],"on":[37,138],"homogeneous":[38],"chaos":[39],"expansion.":[40],"order":[42,112],"approximate":[44],"the":[45,51,58,63,80,86,93,99,106,110,133,142,145,154],"key":[46],"atomic":[47],"operator":[48],"MAX":[49],"in":[50,105,123,153],"full":[52],"random":[53],"space":[54],"during":[55],"analysis,":[57],"adaptively":[61],"chooses":[62],"optimal":[64],"algorithm":[65,118],"from":[66],"a":[67,127],"set":[68],"methods":[72],"considering":[74],"different":[75],"input":[76],"conditions.":[77],"Compared":[78,131],"existing":[81],"methods,":[84],"including":[85],"one":[87,94],"using":[88,95,109],"dimension":[89],"reduction":[90],"technique":[91],"sparse":[96],"grid":[97],"technique,":[98],"has":[102],"10times":[103],"improvements":[104],"accuracy":[107,124],"while":[108],"same":[111],"computation":[114],"time.":[115],"The":[116],"also":[119],"show":[120,148],"great":[121],"improvement":[122],"compared":[125],"moment":[128],"matching":[129],"method.":[130],"10,000":[134],"Monte":[135],"Carlo":[136],"simulations":[137],"ISCAS85":[139],"benchmark":[140],"circuits,":[141],"results":[143],"less":[149],"than":[150],"1%":[151],"error":[152],"mean":[155],"variance,":[157],"nearly":[159],"100times":[160],"speeds":[161],"up.":[162]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}