{"id":"https://openalex.org/W2058463226","doi":"https://doi.org/10.1137/090781231","title":"Deterministic Polynomial Time Algorithms for Matrix Completion Problems","display_name":"Deterministic Polynomial Time Algorithms for Matrix Completion Problems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2058463226","doi":"https://doi.org/10.1137/090781231","mag":"2058463226"},"language":"en","primary_location":{"id":"doi:10.1137/090781231","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090781231","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5050912226","display_name":"G\u00e1bor Ivanyos","orcid":"https://orcid.org/0000-0003-3826-1735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G\u00e1bor Ivanyos","raw_affiliation_strings":["Gabor.Ivanyos@sztaki.hu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gabor.Ivanyos@sztaki.hu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108090276","display_name":"Marek Karpi\u0144ski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marek Karpinski","raw_affiliation_strings":["marek@cs.uni-bonn.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"marek@cs.uni-bonn.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084229662","display_name":"Nitin Saxena","orcid":"https://orcid.org/0000-0001-6931-898X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nitin Saxena","raw_affiliation_strings":["ns@hcm.uni-bonn.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ns@hcm.uni-bonn.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6914,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.8408315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"8","first_page":"3736","last_page":"3751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/matrix","display_name":"Matrix (chemical analysis)","score":0.6001876592636108},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5909903645515442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5868169665336609},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.550719678401947},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5367380976676941},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5123246908187866},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.5002493858337402},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40155673027038574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3846466541290283},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34372952580451965},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12357264757156372},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10142084956169128}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6001876592636108},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5909903645515442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5868169665336609},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.550719678401947},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5367380976676941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5123246908187866},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.5002493858337402},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40155673027038574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3846466541290283},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34372952580451965},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12357264757156372},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10142084956169128},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090781231","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090781231","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W15553240","https://openalex.org/W1533712308","https://openalex.org/W1599026900","https://openalex.org/W1966991151","https://openalex.org/W1969557621","https://openalex.org/W1991963660","https://openalex.org/W1997145001","https://openalex.org/W2011758726","https://openalex.org/W2015555828","https://openalex.org/W2029437570","https://openalex.org/W2034815954","https://openalex.org/W2038660785","https://openalex.org/W2039034730","https://openalex.org/W2044630019","https://openalex.org/W2050735826","https://openalex.org/W2080132708","https://openalex.org/W2090623650","https://openalex.org/W2118187131","https://openalex.org/W2120189374","https://openalex.org/W2123852216","https://openalex.org/W2156209050","https://openalex.org/W2170831059"],"related_works":["https://openalex.org/W3144354057","https://openalex.org/W4301205717","https://openalex.org/W4288107728","https://openalex.org/W2788210652","https://openalex.org/W2108753466","https://openalex.org/W2972830027","https://openalex.org/W4300656036","https://openalex.org/W2611130496","https://openalex.org/W2361403716","https://openalex.org/W2964184729"],"abstract_inverted_index":{"We":[0,113,166,207],"present":[1,293],"new":[2],"deterministic":[3,116,236,295],"algorithms":[4,117],"for":[5,118,211,264],"several":[6],"cases":[7],"of":[8,22,43,78,101,121,124,138,162,171,179,182,214,228,286,288,315],"the":[9,20,26,35,44,79,102,122,136,139,144,169,175,205,255,278,283],"maximum":[10,188,267],"rank":[11,151,189],"matrix":[12,17,32,37,141,172,215,220,257],"completion":[13,40,173,216,258],"problem":[14,21,130,170],"(for":[15,230],"short":[16],"completion),":[18],"i.e.,":[19,222,281],"assigning":[23],"values":[24],"to":[25,33,147,219,225,307],"variables":[27],"in":[28,47,58,135,174,204,223,303],"a":[29,187,193,201,234,241,266,274,289,294],"given":[30,249,290],"symbolic":[31],"maximize":[34],"resulting":[36],"rank.":[38],"Matrix":[39,196],"is":[41,233,251],"one":[42],"fundamental":[45],"problems":[46],"computational":[48],"complexity.":[49],"It":[50],"has":[51],"numerous":[52],"important":[53],"algorithmic":[54],"applications,":[55],"among":[56],"others,":[57],"computing":[59,226],"dynamic":[60],"transitive":[61],"closures":[62],"or":[63,243],"multicast":[64],"network":[65],"codings":[66],"[N.":[67],"J.":[68,91],"A.":[69,92],"Harvey,":[70,93],"D.":[71,94],"R.":[72,95],"Karger,":[73,96],"and":[74,97,126,157,164,185,198,311],"K.":[75],"Murota,":[76],"Proceedings":[77,100],"Sixteenth":[80],"Annual":[81,104],"ACM-SIAM":[82,105],"Symposium":[83,106],"on":[84,107,128],"Discrete":[85,108],"Algorithms,":[86,109],"2005,":[87],"pp.":[88,111],"489\u2013498;":[89],"N.":[90],"S.":[98],"Yekhanin,":[99],"Seventeenth":[103],"2006,":[110],"1103\u20131111].":[112],"design":[114],"efficient":[115],"common":[119],"generalizations":[120],"results":[123,210],"Lov\u00e1sz":[125,163],"Geelen":[127],"this":[129,304],"by":[131,273],"allowing":[132],"linear":[133,180,183],"polynomials":[134],"entries":[137],"input":[140],"such":[142],"that":[143],"submatrices":[145],"corresponding":[146],"each":[148],"variable":[149],"have":[150],"one.":[152],"Our":[153],"methods":[154,301],"are":[155],"algebraic":[156],"quite":[158],"different":[159],"from":[160],"those":[161],"Geelen.":[165],"look":[167],"at":[168],"more":[176],"general":[177,256,309],"setting":[178],"spaces":[181],"transformations":[184],"find":[186],"element":[190],"there":[191,232],"using":[192],"greedy":[194],"method.":[195],"algebras":[197],"modules":[199,229,250,310],"play":[200],"crucial":[202],"role":[203],"algorithm.":[206,298],"show":[208],"(hardness)":[209],"special":[212],"instances":[213],"naturally":[217],"related":[218],"algebras;":[221],"contrast":[224],"isomorphisms":[227],"which":[231],"known":[235],"polynomial":[237,296],"time":[238,297],"algorithm),":[239],"finding":[240,265,282],"surjective":[242],"an":[244],"injective":[245],"homomorphism":[246],"between":[247],"two":[248],"as":[252,254],"hard":[253],"problem.":[259],"The":[260,299],"same":[261],"hardness":[262],"holds":[263],"dimension":[268],"cyclic":[269],"submodule":[270],"(i.e.,":[271],"generated":[272],"single":[275],"element).":[276],"For":[277],"\u201cdual\u201d":[279],"task,":[280],"minimal":[284],"number":[285],"generators":[287],"module,":[291],"we":[292],"proof":[300],"developed":[302],"paper":[305],"apply":[306],"fairly":[308],"could":[312],"also":[313],"be":[314],"independent":[316],"interest.":[317]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
