{"id":"https://openalex.org/W3163628195","doi":"https://doi.org/10.1145/3406325.3451090","title":"Sparse nonnegative convolution is equivalent to dense nonnegative convolution","display_name":"Sparse nonnegative convolution is equivalent to dense nonnegative convolution","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3163628195","doi":"https://doi.org/10.1145/3406325.3451090","mag":"3163628195"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451090","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3406325.3451090","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3406325.3451090","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3406325.3451090","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044394587","display_name":"Karl Bringmann","orcid":"https://orcid.org/0000-0003-1356-5177"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Karl Bringmann","raw_affiliation_strings":["Saarland University, Germany / MPI-INF, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University, Germany / MPI-INF, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102833378","display_name":"Nick Fischer","orcid":"https://orcid.org/0009-0001-0909-3296"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nick Fischer","raw_affiliation_strings":["Saarland University, Germany / MPI-INF, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University, Germany / MPI-INF, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054359620","display_name":"Vasileios Nakos","orcid":"https://orcid.org/0000-0003-2703-2750"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vasileios Nakos","raw_affiliation_strings":["Saarland University, Germany / MPI-INF, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University, Germany / MPI-INF, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05110492,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1711","last_page":"1724"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7537690997123718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7329740524291992},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.609299898147583},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5805721879005432},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.5314815044403076},{"id":"https://openalex.org/keywords/convolution-power","display_name":"Convolution power","score":0.5233765840530396},{"id":"https://openalex.org/keywords/circular-convolution","display_name":"Circular convolution","score":0.5087972283363342},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4680855870246887},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4379903972148895},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4327552914619446},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37952929735183716},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3668453097343445},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34407833218574524},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.15215077996253967},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1384401023387909},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13620328903198242}],"concepts":[{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7537690997123718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7329740524291992},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.609299898147583},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5805721879005432},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.5314815044403076},{"id":"https://openalex.org/C86254553","wikidata":"https://www.wikidata.org/wiki/Q5166605","display_name":"Convolution power","level":5,"score":0.5233765840530396},{"id":"https://openalex.org/C194980680","wikidata":"https://www.wikidata.org/wiki/Q245450","display_name":"Circular convolution","level":5,"score":0.5087972283363342},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4680855870246887},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4379903972148895},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4327552914619446},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37952929735183716},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3668453097343445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34407833218574524},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.15215077996253967},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1384401023387909},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13620328903198242},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3406325.3451090","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3406325.3451090","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3406325.3451090","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2105.05984","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.05984","pdf_url":"https://arxiv.org/pdf/2105.05984","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3163628195","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2105.05984.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2105.05984","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2105.05984","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1145/3406325.3451090","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3406325.3451090","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3406325.3451090","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3163628195.pdf","grobid_xml":"https://content.openalex.org/works/W3163628195.grobid-xml"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W783404226","https://openalex.org/W1480319329","https://openalex.org/W1489355995","https://openalex.org/W1493818369","https://openalex.org/W1514735749","https://openalex.org/W1522964222","https://openalex.org/W1536957917","https://openalex.org/W1562183207","https://openalex.org/W1586217608","https://openalex.org/W1655250744","https://openalex.org/W1943663571","https://openalex.org/W1948197544","https://openalex.org/W1969941659","https://openalex.org/W1978006688","https://openalex.org/W1989204408","https://openalex.org/W1994521750","https://openalex.org/W1996113955","https://openalex.org/W2008249302","https://openalex.org/W2010122118","https://openalex.org/W2010953531","https://openalex.org/W2012365979","https://openalex.org/W2020301027","https://openalex.org/W2022028092","https://openalex.org/W2031683606","https://openalex.org/W2033042165","https://openalex.org/W2049605943","https://openalex.org/W2056559482","https://openalex.org/W2062429446","https://openalex.org/W2070279173","https://openalex.org/W2082051116","https://openalex.org/W2098207812","https://openalex.org/W2099810967","https://openalex.org/W2107625832","https://openalex.org/W2113692647","https://openalex.org/W2136975477","https://openalex.org/W2153517105","https://openalex.org/W2165122343","https://openalex.org/W2168831133","https://openalex.org/W2205172111","https://openalex.org/W2395231588","https://openalex.org/W2537252502","https://openalex.org/W2567351832","https://openalex.org/W2783094551","https://openalex.org/W2793131149","https://openalex.org/W2808759691","https://openalex.org/W2809361502","https://openalex.org/W2903067870","https://openalex.org/W2917327790","https://openalex.org/W2952672079","https://openalex.org/W2959557165","https://openalex.org/W2962847569","https://openalex.org/W2964080237","https://openalex.org/W2965168983","https://openalex.org/W2971607540","https://openalex.org/W2996574036","https://openalex.org/W3018936433","https://openalex.org/W3035306598","https://openalex.org/W3045630729","https://openalex.org/W3101294957","https://openalex.org/W3102065507","https://openalex.org/W3137072739","https://openalex.org/W3186262077","https://openalex.org/W6629617546","https://openalex.org/W6676080805","https://openalex.org/W6685080905","https://openalex.org/W6712397931","https://openalex.org/W6749015919","https://openalex.org/W6750041759","https://openalex.org/W6753020907"],"related_works":["https://openalex.org/W2950942037","https://openalex.org/W2265468072","https://openalex.org/W2432650894","https://openalex.org/W1556308264","https://openalex.org/W1923547365","https://openalex.org/W3037885501","https://openalex.org/W2051573271","https://openalex.org/W2620883762","https://openalex.org/W2953125238","https://openalex.org/W2754246046","https://openalex.org/W2059357470","https://openalex.org/W2963677571","https://openalex.org/W1986545790","https://openalex.org/W2959557165","https://openalex.org/W2624297319","https://openalex.org/W1527447383","https://openalex.org/W1839329870","https://openalex.org/W226380574","https://openalex.org/W2011507771","https://openalex.org/W2005609859"],"abstract_inverted_index":{"Computing":[0],"the":[1,47,53,68],"convolution":[2],"A":[3],"\u22c6":[4],"B":[5,66],"of":[6,21,49,55],"two":[7],"length-n":[8],"vectors":[9],"A,B":[10,56],"is":[11],"an":[12],"ubiquitous":[13],"computational":[14],"primitive,":[15],"with":[16],"applications":[17,27,43],"in":[18,46,75],"a":[19],"variety":[20],"disciplines.":[22],"Within":[23],"theoretical":[24],"computer":[25],"science,":[26],"range":[28],"from":[29,36],"string":[30],"problems":[31],"to":[32,38,63],"Knapsack-type":[33],"problems,":[34],"and":[35,73],"3SUM":[37],"All-Pairs":[39],"Shortest":[40],"Paths.":[41],"These":[42],"often":[44],"come":[45],"form":[48],"nonnegative":[50,58],"convolution,":[51],"where":[52],"entries":[54],"are":[57],"integers.":[59],"The":[60],"classical":[61],"algorithm":[62],"compute":[64],"A\u22c6":[65],"uses":[67],"Fast":[69],"Fourier":[70],"Transform":[71],"(FFT)":[72],"runs":[74],"time":[76],"O(n":[77],"logn).":[78]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}