{"id":"https://openalex.org/W7212258185","doi":"https://doi.org/10.48550/arxiv.2609.11049","title":"A deterministic $(1+\\varepsilon)^n$ approximation for the permanent of a nonnegative matrix","display_name":"A deterministic $(1+\\varepsilon)^n$ approximation for the permanent of a nonnegative matrix","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212258185","doi":"https://doi.org/10.48550/arxiv.2609.11049"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11049","pdf_url":"https://arxiv.org/pdf/2609.11049","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.11049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054551001","display_name":"Dingding Dong","orcid":"https://orcid.org/0000-0001-8500-2897","observed_orcids":["https://orcid.org/0000-0001-8500-2897"]},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dong, Dingding","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science , University of Illinois Chicago , Chicago , IL 60607 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science , University of Illinois Chicago , Chicago , IL 60607 , USA","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017261510","display_name":"Vishesh Jain","orcid":"https://orcid.org/0000-0002-7275-3218","observed_orcids":["https://orcid.org/0000-0002-7275-3218"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jain, Vishesh","raw_affiliation_strings":["Department of Mathematics , California Institute of Technology , Pasadena , CA 91125 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , California Institute of Technology , Pasadena , CA 91125 , USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":9.999999747378752e-05,"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/permanent","display_name":"permanent","score":0.8489999771118164},{"id":"https://openalex.org/keywords/approximation-algorithms","display_name":"approximation algorithms","score":0.6909999847412109},{"id":"https://openalex.org/keywords/deterministic-algorithms","display_name":"deterministic algorithms","score":0.7850000262260437},{"id":"https://openalex.org/keywords/strongly-polynomial-algorithms","display_name":"strongly polynomial algorithms","score":0.9240000247955322},{"id":"https://openalex.org/keywords/nonnegative-matrices","display_name":"nonnegative matrices","score":0.9750000238418579},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.703000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7214000225067139},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41990000009536743},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4072999954223633},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.35280001163482666},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.34880000352859497},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.3249000012874603},{"id":"https://openalex.org/C61987429","wikidata":"https://www.wikidata.org/wiki/Q3064355","display_name":"M-matrix","level":3,"score":0.2962000072002411},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C86761442","wikidata":"https://www.wikidata.org/wiki/Q6787879","display_name":"Matrix method","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25769999623298645}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11049","pdf_url":"https://arxiv.org/pdf/2609.11049","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.11049","doi":"https://doi.org/10.48550/arxiv.2609.11049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11049","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11049","pdf_url":"https://arxiv.org/pdf/2609.11049","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212258185.pdf","grobid_xml":"https://content.openalex.org/works/W7212258185.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1594620223","https://openalex.org/W2037389370","https://openalex.org/W7204805534","https://openalex.org/W7204916796","https://openalex.org/W7207798145","https://openalex.org/W7208733293","https://openalex.org/W7212171764"],"related_works":["https://openalex.org/W226703363","https://openalex.org/W1822909632","https://openalex.org/W7095761188","https://openalex.org/W3142443268","https://openalex.org/W2899996831","https://openalex.org/W4417064297","https://openalex.org/W2162960148","https://openalex.org/W7212171764","https://openalex.org/W4411319968","https://openalex.org/W7204805534"],"abstract_inverted_index":{"For":[0],"every":[1],"fixed":[2],"$0<\\varepsilon\\le1$,":[3],"we":[4],"give":[5],"a":[6,13],"deterministic":[7],"strongly":[8],"polynomial":[9],"algorithm":[10],"that,":[11],"given":[12],"nonnegative":[14],"matrix":[15],"$A\\in\\mathbb{R}_{\\ge0}^{n\\times":[16],"n}$,":[17],"returns":[18],"$Q$":[19],"satisfying":[20],"$\\operatorname{per}":[21],"A\\le":[22],"Q\\le(1+\\varepsilon)^n\\operatorname{per}":[23],"A$.":[24]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}