{"id":"https://openalex.org/W4317496706","doi":"https://doi.org/10.1109/tc.2023.3238128","title":"Towards Globally Optimal Design of Multipliers for FPGAs","display_name":"Towards Globally Optimal Design of Multipliers for FPGAs","publication_year":2023,"publication_date":"2023-01-19","ids":{"openalex":"https://openalex.org/W4317496706","doi":"https://doi.org/10.1109/tc.2023.3238128"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2023.3238128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2023.3238128","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"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 Computers","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/A5056801735","display_name":"Andreas B\u00f6ttcher","orcid":null},"institutions":[{"id":"https://openalex.org/I201850948","display_name":"Fulda University of Applied Sciences","ror":"https://ror.org/041bz9r75","country_code":"DE","type":"education","lineage":["https://openalex.org/I201850948"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas B\u00f6ttcher","raw_affiliation_strings":["Applied Computer Science Department, Fulda University of Applied Sciences, Fulda, Germany"],"affiliations":[{"raw_affiliation_string":"Applied Computer Science Department, Fulda University of Applied Sciences, Fulda, Germany","institution_ids":["https://openalex.org/I201850948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016467458","display_name":"Martin Kumm","orcid":"https://orcid.org/0000-0002-8593-3138"},"institutions":[{"id":"https://openalex.org/I201850948","display_name":"Fulda University of Applied Sciences","ror":"https://ror.org/041bz9r75","country_code":"DE","type":"education","lineage":["https://openalex.org/I201850948"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Kumm","raw_affiliation_strings":["Applied Computer Science Department, Fulda University of Applied Sciences, Fulda, Germany"],"affiliations":[{"raw_affiliation_string":"Applied Computer Science Department, Fulda University of Applied Sciences, Fulda, Germany","institution_ids":["https://openalex.org/I201850948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056801735"],"corresponding_institution_ids":["https://openalex.org/I201850948"],"apc_list":null,"apc_paid":null,"fwci":2.5737,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.89700309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"72","issue":"5","first_page":"1261","last_page":"1273"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9998000264167786,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.8136260509490967},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.7215368747711182},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5794554948806763},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.4977474510669708},{"id":"https://openalex.org/keywords/lookup-table","display_name":"Lookup table","score":0.4974088966846466},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.49653178453445435},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.45488572120666504},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.396453320980072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35326260328292847},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3491417169570923},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.32317379117012024},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.21982142329216003}],"concepts":[{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.8136260509490967},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.7215368747711182},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5794554948806763},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.4977474510669708},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.4974088966846466},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.49653178453445435},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.45488572120666504},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.396453320980072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35326260328292847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3491417169570923},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32317379117012024},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.21982142329216003},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2023.3238128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2023.3238128","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8337926301","display_name":null,"funder_award_id":"426369132","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1605020135","https://openalex.org/W1910331302","https://openalex.org/W1996817998","https://openalex.org/W2018758602","https://openalex.org/W2030898836","https://openalex.org/W2056410596","https://openalex.org/W2067222823","https://openalex.org/W2076793873","https://openalex.org/W2093112037","https://openalex.org/W2102500637","https://openalex.org/W2111010659","https://openalex.org/W2120474114","https://openalex.org/W2126779549","https://openalex.org/W2128061800","https://openalex.org/W2134392548","https://openalex.org/W2151097162","https://openalex.org/W2158958240","https://openalex.org/W2751750437","https://openalex.org/W2761398658","https://openalex.org/W2785117529","https://openalex.org/W2810426084","https://openalex.org/W2915933024","https://openalex.org/W2948244774","https://openalex.org/W2973285591","https://openalex.org/W3035674654","https://openalex.org/W3047131805","https://openalex.org/W3100596846","https://openalex.org/W3140847110","https://openalex.org/W3145668619","https://openalex.org/W3150871057","https://openalex.org/W3166334995","https://openalex.org/W3184537890","https://openalex.org/W6712458530","https://openalex.org/W6727180162"],"related_works":["https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2790557758","https://openalex.org/W2516396101","https://openalex.org/W2024574431","https://openalex.org/W2117300767","https://openalex.org/W1886625815","https://openalex.org/W2374017528","https://openalex.org/W4285503609","https://openalex.org/W2126248441"],"abstract_inverted_index":{"The":[0],"design":[1,17,44],"of":[2,7,22,70,81,89,123,142,154,167,185],"a":[3,58,67,90,120,181],"multiplier":[4,97,165,186],"typically":[5],"consists":[6],"three":[8,28,43,63],"steps:":[9],"(1)":[10],"partial":[11,126],"product":[12,127],"generation,":[13,128],"(2)":[14],"compressor":[15,99],"tree":[16,100],"and":[18,102,130,138],"(3)":[19],"the":[20,23,55,78,87,96,114,136,140,152,192],"selection":[21,105],"final":[24,103,131],"adder.":[25],"Conventionally,":[26],"these":[27],"steps":[29,45,65],"are":[30,38],"performed":[31],"consecutively.":[32],"However,":[33],"when":[34],"targeting":[35],"FPGAs,":[36,156],"there":[37],"many":[39],"possibilities":[40],"in":[41],"all":[42,62],"that":[46,113,157,180],"heavily":[47],"influence":[48],"each":[49],"other.":[50],"This":[51],"proposal":[52],"presents":[53],"for":[54,86,95,119,125,151,164],"first":[56],"time":[57],"holistic":[59],"optimization,":[60],"combining":[61],"optimization":[64],"yielding":[66],"minimum":[68],"amount":[69],"look-up-tables":[71],"(LUTs)":[72],"while":[73],"it":[74],"can":[75,161,188],"also":[76],"guarantee":[77],"minimal":[79],"number":[80,184],"(pipeline)":[82],"stages.":[83],"An":[84],"ILP-formulation":[85],"determination":[88],"combined,":[91],"globally":[92,109,158],"optimal":[93,110,159],"solution":[94,116],"tiling,":[98],"generation":[101],"adder":[104],"is":[106,117,148],"proposed.":[107],"With":[108],"we":[111],"mean":[112],"best":[115],"found":[118],"given":[121],"set":[122],"sub-multipliers":[124],"compressors":[129],"adder.This":[132],"allows":[133],"to":[134,171,191],"improve":[135],"quality":[137],"evaluate":[139],"limitations":[141],"existing":[143],"heuristic":[144],"3-step":[145],"approaches.":[146],"It":[147],"shown":[149],"experimentally":[150],"example":[153],"Xilinx":[155],"solutions":[160],"be":[162,189],"obtained":[163],"sizes":[166],"practical":[168],"relevance,":[169],"leading":[170],"significant":[172],"LUT":[173],"reductions.":[174],"Additional":[175],"packing":[176],"density":[177],"experiments":[178],"show":[179],"significantly":[182],"larger":[183],"instances":[187],"mapped":[190],"same":[193],"device.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":11}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
