{"id":"https://openalex.org/W1982322154","doi":"https://doi.org/10.1137/0401003","title":"Upper and Lower Bounds on Time-Space Tradeoffs for Computations with Embedded Fast Fourier Transforms","display_name":"Upper and Lower Bounds on Time-Space Tradeoffs for Computations with Embedded Fast Fourier Transforms","publication_year":1988,"publication_date":"1988-02-01","ids":{"openalex":"https://openalex.org/W1982322154","doi":"https://doi.org/10.1137/0401003","mag":"1982322154"},"language":"en","primary_location":{"id":"doi:10.1137/0401003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0401003","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5076172610","display_name":"David A. Carlson","orcid":"https://orcid.org/0000-0001-9910-5379"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David A. Carlson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076172610"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09666081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":"1","first_page":"22","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9975000023841858,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9975000023841858,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9894000291824341,"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/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.8796831965446472},{"id":"https://openalex.org/keywords/split-radix-fft-algorithm","display_name":"Split-radix FFT algorithm","score":0.7466985583305359},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6710454821586609},{"id":"https://openalex.org/keywords/prime-factor-fft-algorithm","display_name":"Prime-factor FFT algorithm","score":0.6665713787078857},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6536908149719238},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.6033750772476196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5473341345787048},{"id":"https://openalex.org/keywords/raders-fft-algorithm","display_name":"Rader's FFT algorithm","score":0.5299469232559204},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5055332183837891},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4704738259315491},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41862332820892334},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.39777690172195435},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3878277540206909},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38579288125038147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3436651825904846},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3268177807331085},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.1751420497894287},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.10101562738418579}],"concepts":[{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.8796831965446472},{"id":"https://openalex.org/C103755468","wikidata":"https://www.wikidata.org/wiki/Q17103599","display_name":"Split-radix FFT algorithm","level":5,"score":0.7466985583305359},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6710454821586609},{"id":"https://openalex.org/C77928272","wikidata":"https://www.wikidata.org/wiki/Q7243214","display_name":"Prime-factor FFT algorithm","level":5,"score":0.6665713787078857},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6536908149719238},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.6033750772476196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5473341345787048},{"id":"https://openalex.org/C69598009","wikidata":"https://www.wikidata.org/wiki/Q7280126","display_name":"Rader's FFT algorithm","level":5,"score":0.5299469232559204},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5055332183837891},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4704738259315491},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41862332820892334},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.39777690172195435},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3878277540206909},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38579288125038147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3436651825904846},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3268177807331085},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.1751420497894287},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.10101562738418579},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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":1,"locations":[{"id":"doi:10.1137/0401003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0401003","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W1982912928","https://openalex.org/W1993449345","https://openalex.org/W2004450282","https://openalex.org/W2021496873","https://openalex.org/W2040082402","https://openalex.org/W2063264061","https://openalex.org/W2064136209","https://openalex.org/W2066947547","https://openalex.org/W2134224523","https://openalex.org/W4211197056"],"related_works":["https://openalex.org/W2144412928","https://openalex.org/W2554524608","https://openalex.org/W2977460836","https://openalex.org/W4362564158","https://openalex.org/W2113951268","https://openalex.org/W2031343199","https://openalex.org/W1984254719","https://openalex.org/W2076787260","https://openalex.org/W3046688035","https://openalex.org/W2200032781"],"abstract_inverted_index":{"Computations":[0],"with":[1,38,42,159],"embedded":[2],"Fast":[3],"Fourier":[4],"Transforms":[5],"(FFT)":[6],"have":[7],"many":[8],"important":[9],"applications":[10],"which":[11,70],"include":[12],"high-speed":[13],"polynomial":[14,115,142],"multiplication.":[15,116],"In":[16,28],"this":[17,46],"paper,":[18],"we":[19,30,121],"discuss":[20],"the":[21,32,53,67,84,93,97,104,118,128,156,160],"time-space":[22,85,135,163],"tradeoff":[23,86,136,164],"behavior":[24],"of":[25,35,76,95,99,126],"such":[26,113],"computations.":[27],"particular,":[29],"examine":[31],"way":[33,68],"compositions":[34],"FFT":[36,105,129],"graphs":[37,44,89],"one":[39],"another":[40],"and":[41,107],"other":[43],"affect":[45],"behavior.":[47,87,165],"We":[48,61],"model":[49],"a":[50,77,80,100,141],"computation":[51],"by":[52,103],"well-known":[54],"pebble":[55],"game":[56],"on":[57,83,146],"directed":[58],"acyclic":[59],"graphs.":[60],"are":[62,72],"able":[63],"to":[64,92,108,132,151],"show":[65,122],"that":[66,123,153],"in":[69],"connections":[71],"made":[73],"between":[74],"subgraphs":[75],"graph":[78],"exerts":[79],"nontrivial":[81],"effect":[82],"The":[88],"studied":[90],"correspond":[91],"problem":[94],"finding":[96],"maximum":[98],"vector":[101],"produced":[102],"algorithm,":[106],"problems":[109],"containing":[110],"back-to-back":[111,147],"FFTs":[112,148],"as":[114],"For":[117],"first":[119],"problem,":[120],"different":[124,134],"ways":[125],"expressing":[127],"algorithm":[130,144],"lead":[131],"very":[133],"behaviors.":[137],"Our":[138],"results":[139],"for":[140],"multiplication":[143],"based":[145],"allow":[149],"us":[150],"conclude":[152],"it":[154],"has":[155],"connection":[157],"pattern":[158],"best":[161],"possible":[162]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}