{"id":"https://openalex.org/W2788536085","doi":"https://doi.org/10.1007/s10208-021-09496-x","title":"Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials","display_name":"Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials","publication_year":2021,"publication_date":"2021-04-06","ids":{"openalex":"https://openalex.org/W2788536085","doi":"https://doi.org/10.1007/s10208-021-09496-x","mag":"2788536085"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-021-09496-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09496-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09496-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09496-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078197291","display_name":"Mareike Dressler","orcid":"https://orcid.org/0000-0002-5684-4101"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mareike Dressler","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, 9500 Gilman Drive 0112, La Jolla, CA, 92093-0112, USA","Dept. of Mathematics, University of California, San Diego La Jolla, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive 0112, La Jolla, CA, 92093-0112, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Dept. of Mathematics, University of California, San Diego La Jolla, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089622908","display_name":"Adam Kurpisz","orcid":"https://orcid.org/0000-0002-2320-4482"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Adam Kurpisz","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","Department of Mathematics ETH Zurich  Zurich Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Mathematics ETH Zurich  Zurich Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059450802","display_name":"Timo de Wolff","orcid":"https://orcid.org/0000-0003-0883-1389"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Timo de Wolff","raw_affiliation_strings":["Institut f\u00fcr Analysis und Algebra, AG Algebra, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106, Braunschweig, Germany","Institut f\u00fcr Analysis und Algebra, AG Algebra, Technische Universit\u00e4t Braunschweig, Braunschweig, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Algebra, AG Algebra, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Algebra, AG Algebra, Technische Universit\u00e4t Braunschweig, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078197291"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6058,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.70098142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"2","first_page":"365","last_page":"387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9965000152587891,"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/hypercube","display_name":"Hypercube","score":0.8799534440040588},{"id":"https://openalex.org/keywords/certificate","display_name":"Certificate","score":0.7121785879135132},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6288048028945923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5997365117073059},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5678339004516602},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5281619429588318},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5034381747245789},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4876033365726471},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.44545674324035645},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.42158228158950806},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28292447328567505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.220671147108078}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.8799534440040588},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.7121785879135132},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6288048028945923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5997365117073059},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5678339004516602},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5281619429588318},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5034381747245789},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4876033365726471},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.44545674324035645},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.42158228158950806},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28292447328567505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.220671147108078},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":13,"locations":[{"id":"doi:10.1007/s10208-021-09496-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09496-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09496-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/295617","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/295617","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1802.10004","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.10004","pdf_url":"https://arxiv.org/pdf/1802.10004","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:2788536085","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.10004.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"pmh:oai:drops-oai.dagstuhl.de:9664","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/495053","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/495053","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of Computational Mathematics, 22 (2)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1802.10004","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.10004","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.24451/dspace/11718","is_oa":true,"landing_page_url":"https://doi.org/10.24451/dspace/11718","pdf_url":null,"source":{"id":"https://openalex.org/S7407051224","display_name":"BFH: ARBOR","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.3929/ethz-b-000295617","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000295617","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"},{"id":"doi:10.3929/ethz-b-000495053","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000495053","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"},{"id":"doi:10.4230/lipics.mfcs.2018.82","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.mfcs.2018.82","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":""},{"id":"mag:2964208434","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/mfcs/mfcs2018.html#DresslerKW18","pdf_url":null,"source":{"id":"https://openalex.org/S4306420488","display_name":"Mathematical Foundations of Computer Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Mathematical Foundations of Computer Science","raw_type":null},{"id":"mag:2965615345","is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/opus/volltexte/2018/9664/pdf/LIPIcs-MFCS-2018-82.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s10208-021-09496-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09496-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09496-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1894038239","display_name":"Theory and Applications of Linear and Semidefinite Relaxations for Combinatorial Optimization Problems","funder_award_id":"174117","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4430097687","display_name":null,"funder_award_id":"PZ00P2","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5540742269","display_name":null,"funder_award_id":"WO 2206/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320322958","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2788536085.pdf","grobid_xml":"https://content.openalex.org/works/W2788536085.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W47977097","https://openalex.org/W129224317","https://openalex.org/W1493026726","https://openalex.org/W1568307856","https://openalex.org/W1591868040","https://openalex.org/W1593162480","https://openalex.org/W1597196612","https://openalex.org/W1691008300","https://openalex.org/W1754192177","https://openalex.org/W1870858037","https://openalex.org/W1886138972","https://openalex.org/W1893254807","https://openalex.org/W1967344706","https://openalex.org/W1967821609","https://openalex.org/W1982292900","https://openalex.org/W1985123706","https://openalex.org/W2012805418","https://openalex.org/W2031923588","https://openalex.org/W2033040247","https://openalex.org/W2033515640","https://openalex.org/W2049087128","https://openalex.org/W2053885701","https://openalex.org/W2071727942","https://openalex.org/W2077397558","https://openalex.org/W2078289947","https://openalex.org/W2078561631","https://openalex.org/W2088844265","https://openalex.org/W2095315734","https://openalex.org/W2096547979","https://openalex.org/W2100440346","https://openalex.org/W2120146316","https://openalex.org/W2133404041","https://openalex.org/W2154014787","https://openalex.org/W2156792066","https://openalex.org/W2163925208","https://openalex.org/W2165281529","https://openalex.org/W2168417806","https://openalex.org/W2290522125","https://openalex.org/W2306186691","https://openalex.org/W2321429733","https://openalex.org/W2341022752","https://openalex.org/W2570315187","https://openalex.org/W2574497079","https://openalex.org/W2618217717","https://openalex.org/W2773609948","https://openalex.org/W2808754399","https://openalex.org/W2949580236","https://openalex.org/W2951099296","https://openalex.org/W2953082259","https://openalex.org/W2962902171","https://openalex.org/W2963256102","https://openalex.org/W2963917343","https://openalex.org/W2963946005","https://openalex.org/W3176083298","https://openalex.org/W4231001569","https://openalex.org/W4231868828","https://openalex.org/W4232911618","https://openalex.org/W4233252806","https://openalex.org/W4240837394","https://openalex.org/W4255442211","https://openalex.org/W4298289021"],"related_works":["https://openalex.org/W2965615345","https://openalex.org/W2239251014","https://openalex.org/W2963917343","https://openalex.org/W2895618514","https://openalex.org/W2799036797","https://openalex.org/W1982292900","https://openalex.org/W2996749050","https://openalex.org/W2997540580","https://openalex.org/W2964239200","https://openalex.org/W2766126646","https://openalex.org/W2613176042","https://openalex.org/W2595078190","https://openalex.org/W2016687122","https://openalex.org/W2949673399","https://openalex.org/W1617341369","https://openalex.org/W2011603435","https://openalex.org/W3022243219","https://openalex.org/W1988025893","https://openalex.org/W1655278162","https://openalex.org/W2031539449"],"abstract_inverted_index":{"Abstract":[0],"Various":[1],"key":[2,68],"problems":[3,14,31,48],"from":[4,198],"theoretical":[5],"computer":[6],"science":[7],"can":[8],"be":[9],"expressed":[10],"as":[11,39],"polynomial":[12,124],"optimization":[13,47,204],"over":[15,49,81,125],"the":[16,50,82,126,167,200,203],"boolean":[17,51,85,127],"hypercube.":[18],"One":[19],"particularly":[20],"successful":[21],"way":[22],"to":[23,165,189],"prove":[24,161],"complexity":[25],"bounds":[26],"for":[27,70,76,120,181,192],"these":[28,196],"types":[29],"of":[30,36,60,89,97,122,177],"is":[32,170],"based":[33],"on":[34],"sums":[35,59],"squares":[37],"(SOS)":[38],"nonnegativity":[40,121],"certificates.":[41],"In":[42],"this":[43],"article,":[44],"we":[45,160],"initiate":[46],"hypercube":[52,86],"via":[53],"a":[54,94,115,123,133],"recent,":[55],"alternative":[56],"certificate":[57,96,119,138],"called":[58],"nonnegative":[61,80,156],"circuit":[62,157],"polynomials":[63],"(SONC).":[64],"We":[65,194],"show":[66],"that":[67,139,180],"results":[69,197],"SOS-based":[71],"certificates":[72],"remain":[73],"valid:":[74],"First,":[75],"polynomials,":[77],"which":[78],"are":[79],"n":[83],"-variate":[84],"with":[87],"constraints":[88],"degree":[90,98,116,135],"d":[91,117,136],"there":[92,113,130,183],"exists":[93,114,132],"SONC":[95,118,137,168,182],"at":[99,141],"most":[100,142],"$$n+d$$":[101],"<mml:math":[102,144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[103,145],"<mml:mrow>":[104,148],"<mml:mi>n</mml:mi>":[105,147],"<mml:mo>+</mml:mo>":[106],"<mml:mi>d</mml:mi>":[107,151],"</mml:mrow>":[108,153],"</mml:math>":[109,155],".":[110],"Second,":[111],"if":[112],"hypercube,":[128],"then":[129],"also":[131],"short":[134],"includes":[140],"$$n^{O(d)}$$":[143],"<mml:msup>":[146],"<mml:mi>O</mml:mi>":[149],"<mml:mo>(</mml:mo>":[150],"<mml:mo>)</mml:mo>":[152],"</mml:msup>":[154],"polynomials.":[158],"Moreover,":[159],"that,":[162],"in":[163],"opposite":[164],"SOS,":[166],"cone":[169],"not":[171,185],"closed":[172],"under":[173],"taking":[174],"affine":[175],"transformation":[176],"variables":[178],"and":[179,202],"does":[184],"exist":[186],"an":[187],"equivalent":[188],"Putinar\u2019s":[190],"Positivstellensatz":[191],"SOS.":[193],"discuss":[195],"both":[199],"algebraic":[201],"perspective.":[205]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
