{"id":"https://openalex.org/W1505281405","doi":"https://doi.org/10.1007/11499107_22","title":"Sums of Squares, Satisfiability and Maximum Satisfiability","display_name":"Sums of Squares, Satisfiability and Maximum Satisfiability","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1505281405","doi":"https://doi.org/10.1007/11499107_22","mag":"1505281405"},"language":"en","primary_location":{"id":"doi:10.1007/11499107_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11499107_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5084566377","display_name":"Hans van Maaren","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hans van Maaren","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006121874","display_name":"Linda van Norden","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Linda van Norden","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.0625,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92727273,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"294","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9955000281333923,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9911999702453613,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8304734230041504},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.6679373383522034},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6678894758224487},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6519603729248047},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.5872160196304321},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5768294930458069},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5397487878799438},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5391130447387695},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5361616015434265},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.5135024189949036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4875006377696991},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4423278272151947},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42935484647750854},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.4268917441368103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27549582719802856},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21805474162101746},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.09933581948280334},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.07855698466300964},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.06070038676261902}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8304734230041504},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6679373383522034},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6678894758224487},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6519603729248047},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5872160196304321},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5768294930458069},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5397487878799438},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5391130447387695},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5361616015434265},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.5135024189949036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4875006377696991},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4423278272151947},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42935484647750854},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.4268917441368103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27549582719802856},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21805474162101746},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.09933581948280334},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.07855698466300964},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.06070038676261902},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/11499107_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11499107_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.5830","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.5830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jsat.ewi.tudelft.nl/addendum/SDPaddendumSOS.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.7734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.7734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isa.ewi.tudelft.nl/~heule/publications/sum_of_squares.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W423970876","https://openalex.org/W1549186681","https://openalex.org/W1576805635","https://openalex.org/W1581661059","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1985123706","https://openalex.org/W1987579904","https://openalex.org/W1999032440","https://openalex.org/W1999613943","https://openalex.org/W2071727942","https://openalex.org/W2074116126","https://openalex.org/W2109039359","https://openalex.org/W2137373403","https://openalex.org/W2506277857","https://openalex.org/W2752853835","https://openalex.org/W2949673622","https://openalex.org/W2962725330","https://openalex.org/W4245266864"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W4298028631","https://openalex.org/W2264889489","https://openalex.org/W2964111768","https://openalex.org/W2771160919","https://openalex.org/W4301659259"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
