{"id":"https://openalex.org/W336654736","doi":"https://doi.org/10.1016/s0304-3975(99)00185-1","title":"Some structural properties of low-rank matrices related to computational complexity","display_name":"Some structural properties of low-rank matrices related to computational complexity","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W336654736","doi":"https://doi.org/10.1016/s0304-3975(99)00185-1","mag":"336654736"},"language":"en","primary_location":{"id":"doi:10.1016/s0304-3975(99)00185-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(99)00185-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"type":"article","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/A5075201778","display_name":"Bruno Codenotti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruno Codenotti","raw_affiliation_strings":["Istituto Matematica Computazionale, Consiglio Naz. \u201cdella Ricerche\u201d, Via S. Maria 46, 56126-Pisa, Italy","Istituto Matematica Computazionale, Pisa, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Istituto Matematica Computazionale, Consiglio Naz. \u201cdella Ricerche\u201d, Via S. Maria 46, 56126-Pisa, Italy","institution_ids":[]},{"raw_affiliation_string":"Istituto Matematica Computazionale, Pisa, Italy#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109848440","display_name":"Pavel Pudl\u00e1k","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Pavel Pudl\u00e1k","raw_affiliation_strings":["Mathematical Institute, AV\u010cR, \u017ditn\u00e1 25, 115 67 Praha 1, Czech Republic","Mathematical Institute, Czech Republic#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, AV\u010cR, \u017ditn\u00e1 25, 115 67 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I4210120266"]},{"raw_affiliation_string":"Mathematical Institute, Czech Republic#TAB#","institution_ids":["https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081575220","display_name":"Giovanni Resta","orcid":"https://orcid.org/0000-0003-1315-2700"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giovanni Resta","raw_affiliation_strings":["Istituto Matematica Computazionale, Consiglio Naz. \u201cdella Ricerche\u201d, Via S. Maria 46, 56126-Pisa, Italy","Istituto Matematica Computazionale, Pisa, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Istituto Matematica Computazionale, Consiglio Naz. \u201cdella Ricerche\u201d, Via S. Maria 46, 56126-Pisa, Italy","institution_ids":[]},{"raw_affiliation_string":"Istituto Matematica Computazionale, Pisa, Italy#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081575220"],"corresponding_institution_ids":[],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.01956616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"235","issue":"1","first_page":"89","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9868999719619751,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9861000180244446,"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/sublinear-function","display_name":"Sublinear function","score":0.9151265621185303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7338642477989197},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6653574705123901},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6215826272964478},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6206169128417969},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5955364108085632},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5867143273353577},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.5246691703796387},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5084201693534851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4676980972290039},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4484371244907379},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.43147075176239014},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.414357453584671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10932174324989319}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.9151265621185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7338642477989197},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6653574705123901},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6215826272964478},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6206169128417969},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5955364108085632},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5867143273353577},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5246691703796387},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5084201693534851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4676980972290039},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4484371244907379},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.43147075176239014},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.414357453584671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10932174324989319},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1016/s0304-3975(99)00185-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(99)00185-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.10.1032","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.1032","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eccc.uni-trier.de/eccc-reports/1997/TR97-043/Paper.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.35.8438","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.8438","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1997/TR97-043/pub/eccc/reports/1997/TR97-043/Paper.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.795","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.795","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1997/TR97-043/revisn01.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.9311","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.9311","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imc.pi.cnr.it/~brunoc/ps_files/TCS_LAST.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.7060","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.7060","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cas.cz/~pudlak/onsome.ps","raw_type":"text"},{"id":"mag:336654736","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc4.html#ECCC-TR97-043","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W181128013","https://openalex.org/W1530008367","https://openalex.org/W1623354552","https://openalex.org/W1974827405","https://openalex.org/W2003447360","https://openalex.org/W2008671178","https://openalex.org/W2016341899","https://openalex.org/W2029734507","https://openalex.org/W2056829476","https://openalex.org/W2070359427","https://openalex.org/W2079175807","https://openalex.org/W2090746613","https://openalex.org/W2136813926","https://openalex.org/W2140469501","https://openalex.org/W2609005943","https://openalex.org/W4299798129"],"related_works":["https://openalex.org/W1969872431","https://openalex.org/W2024500982","https://openalex.org/W2543706324","https://openalex.org/W2137079479","https://openalex.org/W3109471745","https://openalex.org/W3211045668","https://openalex.org/W2590781157","https://openalex.org/W3197152554","https://openalex.org/W3165296918","https://openalex.org/W2737871803","https://openalex.org/W2041960351","https://openalex.org/W3196449631","https://openalex.org/W2979727130","https://openalex.org/W2770218907","https://openalex.org/W3139676462","https://openalex.org/W3187884296","https://openalex.org/W3013106083","https://openalex.org/W2893988113","https://openalex.org/W2140451017","https://openalex.org/W2773058504"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}