{"id":"https://openalex.org/W2005629337","doi":"https://doi.org/10.1107/s010876730501648x","title":"Polynomial-time algorithms for the integer minimal principle for centrosymmetric structures","display_name":"Polynomial-time algorithms for the integer minimal principle for centrosymmetric structures","publication_year":2005,"publication_date":"2005-06-23","ids":{"openalex":"https://openalex.org/W2005629337","doi":"https://doi.org/10.1107/s010876730501648x","mag":"2005629337","pmid":"https://pubmed.ncbi.nlm.nih.gov/15972998"},"language":"en","primary_location":{"id":"doi:10.1107/s010876730501648x","doi":"https://doi.org/10.1107/s010876730501648x","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s010876730501648x","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"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/A5043025702","display_name":"Anastasia Vaia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anastasia Vaia","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031811254","display_name":"Nikolaos V. Sahinidis","orcid":"https://orcid.org/0000-0003-2087-9131","observed_orcids":["https://orcid.org/0000-0003-2087-9131"]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikolaos V. Sahinidis","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801 USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.4063,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59602538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"4","first_page":"445","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12613","display_name":"X-ray Diffraction in Crystallography","score":0.8871999979019165,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12613","display_name":"X-ray Diffraction in Crystallography","score":0.8871999979019165,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11162","display_name":"Enzyme Structure and Function","score":0.061900001019239426,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10464","display_name":"Crystal structures of chemical compounds","score":0.024800000712275505,"subfield":{"id":"https://openalex.org/subfields/1604","display_name":"Inorganic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/centrosymmetric-structure","display_name":"centrosymmetric structure","score":0.9399999976158142},{"id":"https://openalex.org/keywords/single-crystal-x-ray-diffraction","display_name":"single-crystal X-ray diffraction","score":0.9139999747276306},{"id":"https://openalex.org/keywords/phase-problem","display_name":"phase problem","score":0.7979999780654907},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.7009999752044678},{"id":"https://openalex.org/keywords/reciprocal-space","display_name":"reciprocal space","score":0.6259999871253967},{"id":"https://openalex.org/keywords/global-optimality","display_name":"global optimality","score":0.7170000076293945},{"id":"https://openalex.org/keywords/crystal-structure-determination","display_name":"crystal structure determination","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.699254035949707},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.6716493368148804},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.6030580401420593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5324861407279968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5245309472084045},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47520527243614197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4267118573188782},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3707839250564575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31354576349258423},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13306638598442078},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015394","descriptor_name":"Molecular Structure","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1107/s010876730501648x","doi":"https://doi.org/10.1107/s010876730501648x","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s010876730501648x","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},{"id":"pmid:15972998","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/15972998","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta crystallographica. Section A, Foundations of crystallography","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1773990982","display_name":null,"funder_award_id":"GM072023","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G3191170182","display_name":"Novel Algorithms for Crystallographic Computing","funder_award_id":"R01GM072023","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1985114052","https://openalex.org/W1985940079","https://openalex.org/W2016781185","https://openalex.org/W2057978182","https://openalex.org/W2070822826","https://openalex.org/W2077999356","https://openalex.org/W2097578445","https://openalex.org/W2148066840"],"related_works":["https://openalex.org/W2077999356","https://openalex.org/W2092256999","https://openalex.org/W2586419471","https://openalex.org/W3000203171","https://openalex.org/W2086154537","https://openalex.org/W1603688087","https://openalex.org/W2506266366","https://openalex.org/W2320297149","https://openalex.org/W2408582788","https://openalex.org/W2315293775"],"abstract_inverted_index":{"The":[0],"minimal":[1,43,79],"principle":[2,44,80],"for":[3,21,178,192],"structure":[4],"determination":[5],"from":[6],"single-crystal":[7],"X-ray":[8],"diffraction":[9],"measurements":[10],"has":[11],"recently":[12],"been":[13],"formulated":[14],"as":[15,101],"an":[16,57,89],"integer":[17,52,78],"linear":[18,123],"optimization":[19,90,99,117],"model":[20,30],"the":[22,37,42,64,77,86,95,98,116,126,151,165,175],"case":[23],"of":[24,28,41,60,88,94,97,107,122,129,145,153,160],"centrosymmetric":[25,179],"structures.":[26,180],"Solution":[27],"this":[29,68,143],"via":[31],"established":[32],"combinatorial":[33],"branch-and-bound":[34],"algorithms":[35,137],"provides":[36,168],"true":[38],"global":[39,82],"minimum":[40],"while":[45],"operating":[46],"exclusively":[47],"in":[48,103,112,125,147,150],"reciprocal":[49],"space.":[50,66],"However,":[51],"programming":[53],"techniques":[54],"may":[55],"require":[56],"exponential":[58],"number":[59,106,127,152],"iterations":[61],"to":[62,75,81,114,119,141,174],"exhaust":[63],"search":[65],"In":[67],"paper,":[69],"a":[70,104,120,158],"new":[71],"approach":[72,167,182],"is":[73],"developed":[74,140],"solve":[76,142],"optimality":[83],"without":[84],"requiring":[85],"solution":[87,96],"problem.":[91],"Instead,":[92],"properties":[93],"problem,":[100],"observed":[102],"large":[105],"computational":[108],"experiments,":[109],"are":[110,138],"exploited":[111],"order":[113],"reduce":[115],"formulation":[118],"system":[121,144],"equations":[124,146],"field":[128],"two":[130],"elements":[131],"(F(2)).":[132],"Two":[133],"specialized":[134],"Gaussian":[135],"elimination":[136],"then":[139],"polynomial":[148],"time":[149],"atoms.":[154],"Computational":[155],"results":[156],"on":[157],"collection":[159],"38":[161,194],"structures":[162,195],"demonstrate":[163],"that":[164],"proposed":[166],"very":[169],"fast":[170],"and":[171],"accurate":[172],"solutions":[173],"phase":[176],"problem":[177],"This":[181],"also":[183],"provided":[184],"much":[185],"better":[186],"crystallographic":[187],"R":[188],"values":[189],"than":[190],"SHELXS":[191],"all":[193],"tested.":[196]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}
