{"id":"https://openalex.org/W2997850323","doi":"https://doi.org/10.1137/20m1351692","title":"Exact Semidefinite Programming Bounds for Packing Problems","display_name":"Exact Semidefinite Programming Bounds for Packing Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2997850323","doi":"https://doi.org/10.1137/20m1351692","mag":"2997850323"},"language":"en","primary_location":{"id":"doi:10.1137/20m1351692","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351692","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.00256","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033419402","display_name":"Maria Dostert","orcid":"https://orcid.org/0000-0002-0393-8286"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Maria Dostert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061628061","display_name":"David de Laat","orcid":"https://orcid.org/0000-0002-5178-1906"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David de Laat","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5178-1906","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046269354","display_name":"Philippe Moustrou","orcid":"https://orcid.org/0000-0003-3432-4954"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philippe Moustrou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033419402"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00983021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"2","first_page":"1433","last_page":"1458"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","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/T12404","display_name":"Mathematical Approximation and Integration","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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7899699211120605},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7489513158798218},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7012629508972168},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5343586206436157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5329462289810181},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.5209947228431702},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4891939163208008},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.48594653606414795},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45869937539100647},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4538666903972626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33449286222457886},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25081759691238403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17410480976104736},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1256931722164154},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10735675692558289},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09242367744445801}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7899699211120605},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7489513158798218},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7012629508972168},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5343586206436157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5329462289810181},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5209947228431702},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4891939163208008},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.48594653606414795},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45869937539100647},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4538666903972626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33449286222457886},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25081759691238403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17410480976104736},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1256931722164154},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10735675692558289},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09242367744445801},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/20m1351692","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351692","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2001.00256","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00256","pdf_url":"https://arxiv.org/pdf/2001.00256","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":"","raw_type":"text"},{"id":"mag:2997850323","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.00256v3","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:HAL:hal-03408746v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03408746","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2021, 31 (2), pp.1433-1458. &#x27E8;10.1137/20M1351692&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:munin.uit.no:10037/24531","is_oa":true,"landing_page_url":"https://hdl.handle.net/10037/24531","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2001.00256","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.00256","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.00256","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00256","pdf_url":"https://arxiv.org/pdf/2001.00256","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1786514303","display_name":null,"funder_award_id":"DMS-1439786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4647115361","display_name":null,"funder_award_id":"17matteCR","funder_id":"https://openalex.org/F4320309820","funder_display_name":"Universitetet i Troms\u00f8"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309820","display_name":"Universitetet i Troms\u00f8","ror":"https://ror.org/00wge5k78"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1512840059","https://openalex.org/W1945716106","https://openalex.org/W1963785789","https://openalex.org/W1982216340","https://openalex.org/W1983655075","https://openalex.org/W1995320256","https://openalex.org/W2013083117","https://openalex.org/W2016389104","https://openalex.org/W2018627370","https://openalex.org/W2029734006","https://openalex.org/W2032980094","https://openalex.org/W2039539620","https://openalex.org/W2042323836","https://openalex.org/W2055993677","https://openalex.org/W2079565519","https://openalex.org/W2095694172","https://openalex.org/W2101504517","https://openalex.org/W2119346580","https://openalex.org/W2120575449","https://openalex.org/W2120788459","https://openalex.org/W2140695699","https://openalex.org/W2141040012","https://openalex.org/W2145139206","https://openalex.org/W2260541623","https://openalex.org/W2268390549","https://openalex.org/W2584020404","https://openalex.org/W2734887310","https://openalex.org/W2903807795","https://openalex.org/W2905003027","https://openalex.org/W2962893120","https://openalex.org/W2963419410","https://openalex.org/W2964067925","https://openalex.org/W3010831251","https://openalex.org/W3098957505","https://openalex.org/W3099246670","https://openalex.org/W3100072452","https://openalex.org/W3124734834","https://openalex.org/W3139681725","https://openalex.org/W4255317205","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W3100072452","https://openalex.org/W2952690984","https://openalex.org/W2964963376","https://openalex.org/W1993661885","https://openalex.org/W2960468055","https://openalex.org/W2072918044","https://openalex.org/W1541505008","https://openalex.org/W3165501148","https://openalex.org/W2964000362","https://openalex.org/W2188680895","https://openalex.org/W2158834326","https://openalex.org/W1007879714","https://openalex.org/W2963814313","https://openalex.org/W2971982775","https://openalex.org/W2950631834","https://openalex.org/W1540861457","https://openalex.org/W2950029189","https://openalex.org/W3101014297","https://openalex.org/W2949964558","https://openalex.org/W3172548086"],"abstract_inverted_index":{"In":[0,59],"this":[1,33],"paper":[2],"we":[3,42,61,89],"give":[4],"an":[5],"algorithm":[6],"to":[7,18,34,47,57,114,122],"round":[8],"the":[9,22,29,64,68,73,83,92,96,128],"floating":[10],"point":[11],"output":[12],"of":[13,28,130],"a":[14,19,25,137],"semidefinite":[15],"programming":[16],"solver":[17],"solution":[20],"over":[21],"rationals":[23],"or":[24],"quadratic":[26],"extension":[27],"rationals.":[30],"We":[31,117],"apply":[32],"get":[35],"sharp":[36,45,111,124],"bounds":[37,46,126],"for":[38,95],"packing":[39,52],"problems,":[40],"and":[41,88],"use":[43,119],"these":[44],"prove":[48,90],"that":[49,63,91,105,132],"certain":[50],"optimal":[51,75],"configurations":[53],"are":[54],"unique":[55,74],"up":[56],"rotations.":[58],"particular,":[60],"show":[62],"configuration":[65],"coming":[66],"from":[67],"$\\mathsf{E}_8$":[69],"root":[70],"lattice":[71],"is":[72,103,110],"code":[76],"with":[77],"minimal":[78],"angular":[79],"distance":[80],"$\u03c0/3$":[81],"on":[82,127],"hemisphere":[84],"in":[85],"$\\mathbb":[86,115],"R^8$,":[87],"three-point":[93],"bound":[94],"$(3,":[97],"8,":[98],"\\vartheta)$-spherical":[99],"code,":[100],"where":[101],"$\\vartheta$":[102],"such":[104],"$\\cos":[106],"\\vartheta":[107],"=":[108],"(2\\sqrt{2}-1)/7$,":[109],"by":[112],"rounding":[113],"Q[\\sqrt{2}]$.":[116],"also":[118],"our":[120],"machinery":[121],"compute":[123],"upper":[125],"number":[129],"spheres":[131],"can":[133],"be":[134],"packed":[135],"into":[136],"larger":[138],"sphere.":[139]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
