{"id":"https://openalex.org/W1554495759","doi":"https://doi.org/10.1007/978-3-540-30538-5_20","title":"On the Complexity of Hilbert\u2019s 17th Problem","display_name":"On the Complexity of Hilbert\u2019s 17th Problem","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1554495759","doi":"https://doi.org/10.1007/978-3-540-30538-5_20","mag":"1554495759"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-30538-5_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-30538-5_20","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":"book-chapter","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/A5060217026","display_name":"Nikhil R. Devanur","orcid":"https://orcid.org/0009-0005-4406-5935"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nikhil R. Devanur","raw_affiliation_strings":["College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332"],"affiliations":[{"raw_affiliation_string":"College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109812838","display_name":"Richard J. Lipton","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard J. Lipton","raw_affiliation_strings":["College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332"],"affiliations":[{"raw_affiliation_string":"College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063089732","display_name":"Nisheeth K. Vishnoi","orcid":"https://orcid.org/0000-0002-0255-1119"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nisheeth K. Vishnoi","raw_affiliation_strings":["College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332"],"affiliations":[{"raw_affiliation_string":"College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060217026"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0258,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.81832928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"237","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9975000023841858,"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":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8040363788604736},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.46823850274086},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4240497648715973},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3573920726776123},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31014055013656616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14323076605796814},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08682560920715332}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8040363788604736},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.46823850274086},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4240497648715973},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3573920726776123},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31014055013656616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14323076605796814},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08682560920715332}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-540-30538-5_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-30538-5_20","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:10.1.1.190.2833","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.2833","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/um/people/nikdev/pubs/hilbert.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.491.1277","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.491.1277","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/um/people/nvishno/site/publications_files/dlv05fsttcs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.9808","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.9808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cc.gatech.edu/~nikhil/pubs/hilbert.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":35,"referenced_works":["https://openalex.org/W12342701","https://openalex.org/W197661341","https://openalex.org/W201320490","https://openalex.org/W618938044","https://openalex.org/W1506247181","https://openalex.org/W1539838732","https://openalex.org/W1591868040","https://openalex.org/W1731990723","https://openalex.org/W1823367140","https://openalex.org/W1975442866","https://openalex.org/W1987458144","https://openalex.org/W2011039300","https://openalex.org/W2011758726","https://openalex.org/W2019578639","https://openalex.org/W2036265926","https://openalex.org/W2047577886","https://openalex.org/W2052168717","https://openalex.org/W2065053468","https://openalex.org/W2066356146","https://openalex.org/W2071040500","https://openalex.org/W2071727942","https://openalex.org/W2077202644","https://openalex.org/W2085352155","https://openalex.org/W2111028162","https://openalex.org/W2132605415","https://openalex.org/W2401610261","https://openalex.org/W2745281314","https://openalex.org/W3141205388","https://openalex.org/W3145855177","https://openalex.org/W3148554666","https://openalex.org/W4213009134","https://openalex.org/W4233252806","https://openalex.org/W4244999758","https://openalex.org/W4285719527","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2189341500"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}