{"id":"https://openalex.org/W2578305700","doi":"https://doi.org/10.1007/s00037-020-00200-z","title":"Linear Matroid Intersection is in Quasi-NC","display_name":"Linear Matroid Intersection is in Quasi-NC","publication_year":2017,"publication_date":"2017-06-15","ids":{"openalex":"https://openalex.org/W2578305700","doi":"https://doi.org/10.1007/s00037-020-00200-z","mag":"2578305700"},"language":"en","primary_location":{"id":"doi:10.1007/s00037-020-00200-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-020-00200-z","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","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/A5102842266","display_name":"Rohit Gurjar","orcid":"https://orcid.org/0000-0002-8623-0872"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Rohit Gurjar","raw_affiliation_strings":["Department of Computer Science\nand Engineering, Indian Institute of Technology\nBombay, Mumbai, MH, 400076, India","Department of Computer Science#N#and Engineering, Indian Institute of Technology#N#Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science\nand Engineering, Indian Institute of Technology\nBombay, Mumbai, MH, 400076, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Computer Science#N#and Engineering, Indian Institute of Technology#N#Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029341628","display_name":"Thomas Thierauf","orcid":"https://orcid.org/0000-0002-2962-594X"},"institutions":[{"id":"https://openalex.org/I4210136950","display_name":"Hochschule Aalen","ror":"https://ror.org/04gg60e72","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210136950"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Thierauf","raw_affiliation_strings":["Faculty of Electronics and\nComputer Science, Aalen University, 73430, Aalen, Germany","Faculty of Electronics and#N#Computer Science, Aalen University, Aalen, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Electronics and\nComputer Science, Aalen University, 73430, Aalen, Germany","institution_ids":["https://openalex.org/I4210136950"]},{"raw_affiliation_string":"Faculty of Electronics and#N#Computer Science, Aalen University, Aalen, Germany","institution_ids":["https://openalex.org/I4210136950"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102842266"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.9085,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75195833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"2","first_page":"821","last_page":"830"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"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/matroid","display_name":"Matroid","score":0.93112713098526},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6985577940940857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6867517232894897},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.6070941686630249},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5790836215019226},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5363529920578003},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5197526812553406},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5118154883384705},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4842524230480194},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4832976162433624},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45528870820999146},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4513876736164093},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.4203186333179474},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.41185683012008667},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.38411498069763184},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0939071774482727}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.93112713098526},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6985577940940857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6867517232894897},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.6070941686630249},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5790836215019226},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5363529920578003},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5197526812553406},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5118154883384705},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4842524230480194},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4832976162433624},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45528870820999146},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4513876736164093},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.4203186333179474},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.41185683012008667},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38411498069763184},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0939071774482727},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00037-020-00200-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-020-00200-z","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"},{"id":"doi:10.1145/3055399.3055440","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3055399.3055440","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:opus-htw-aalen.bsz-bw.de:1928","is_oa":false,"landing_page_url":"https://opus-htw-aalen.bsz-bw.de/frontdoor/index/index/docId/1928","pdf_url":null,"source":{"id":"https://openalex.org/S4306401044","display_name":"OPUS (Aalen University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"mag:2578305700","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc23.html#GurjarT16","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W247221977","https://openalex.org/W1503731768","https://openalex.org/W1570807665","https://openalex.org/W1571321110","https://openalex.org/W1599026900","https://openalex.org/W1939881310","https://openalex.org/W1968245619","https://openalex.org/W1979726029","https://openalex.org/W2015555828","https://openalex.org/W2050735826","https://openalex.org/W2056352038","https://openalex.org/W2058463226","https://openalex.org/W2064885856","https://openalex.org/W2080132708","https://openalex.org/W2081256023","https://openalex.org/W2082002555","https://openalex.org/W2087311268","https://openalex.org/W2090623650","https://openalex.org/W2091564680","https://openalex.org/W2098265073","https://openalex.org/W2113622785","https://openalex.org/W2123852216","https://openalex.org/W2165621523","https://openalex.org/W2169974244","https://openalex.org/W2170831059","https://openalex.org/W2309721867","https://openalex.org/W2399980850","https://openalex.org/W2578305700","https://openalex.org/W2610479830","https://openalex.org/W2742794645","https://openalex.org/W2981568733","https://openalex.org/W2988480584","https://openalex.org/W4234130962","https://openalex.org/W6820289075"],"related_works":["https://openalex.org/W2295819159","https://openalex.org/W2011193572","https://openalex.org/W2951145498","https://openalex.org/W2903540361","https://openalex.org/W2042977557","https://openalex.org/W1618878876","https://openalex.org/W3129024859","https://openalex.org/W2063951771","https://openalex.org/W2963410133","https://openalex.org/W2904152387","https://openalex.org/W2170054126","https://openalex.org/W2123734400","https://openalex.org/W2902143576","https://openalex.org/W2963204136","https://openalex.org/W2953059252","https://openalex.org/W2611242280","https://openalex.org/W3139496137","https://openalex.org/W2093776691","https://openalex.org/W1691921959","https://openalex.org/W2951838648"],"abstract_inverted_index":{"Given":[0],"two":[1,118],"matroids":[2,225],"on":[3],"the":[4,8,27,50,73,76,96,108,112,147,152,190,204,221],"same":[5],"ground":[6],"set,":[7],"matroid":[9,52],"intersection":[10,53],"problem":[11,28,54],"asks":[12],"to":[13,81,106,125,203,215],"find":[14,216],"a":[15,30,92,127,133,143,183,200,217],"common":[16,115],"independent":[17],"set":[18],"of":[19,24,44,64,75,86,114,117,136,142,151,196,223],"maximum":[20,205],"size.":[21],"In":[22],"case":[23,85,135],"linear":[25,51,224],"matroids,":[26],"had":[29],"randomized":[31],"parallel":[32],"algorithm":[33,131,188],"but":[34],"no":[35],"deterministic":[36,201,218],"one.":[37],"We":[38,120],"give":[39,126],"an":[40,165],"almost":[41],"complete":[42],"derandomization":[43],"this":[45,197],"algorithm,":[46],"which":[47],"implies":[48],"that":[49],"is":[55,105,150,199],"in":[56,84,226],"quasi-NC.":[57,227],"That":[58],"is,":[59],"it":[60],"has":[61],"uniform":[62],"circuits":[63],"quasi-polynomial":[65,128],"size":[66],"$$n^{O(\\log":[67],"n)}$$":[68],"and":[69,169],"O(polylog(n))":[70],"depth.":[71],"Moreover,":[72],"depth":[74],"circuit":[77],"can":[78,178],"be":[79,180],"reduced":[80],"O(log2":[82],"n)":[83],"zero":[87],"characteristic":[88],"fields.":[89],"This":[90,177],"generalizes":[91],"similar":[93],"result":[94,124,198,214],"for":[95,111,132,164,189,220],"bipartite":[97],"perfect":[98],"matching":[99],"problem.":[100,209],"Our":[101],"main":[102],"technical":[103],"contribution":[104],"derandomize":[107],"Isolation":[109],"lemma":[110],"family":[113],"bases":[116],"matroids.":[119],"use":[121,212],"our":[122,213],"isolation":[123],"time":[129],"blackbox":[130,184],"special":[134],"Edmonds'":[137],"problem,":[138],"i.e.,":[139],"singularity":[140],"testing":[141,187],"symbolic":[144],"matrix,":[145],"when":[146],"given":[148],"matrix":[149,167,207],"form":[153],"$$A_{0}":[154],"+":[155,158,160],"A_{1":[156],"}x_{1}":[157],"\\cdots":[159],"A_{m}":[161],"x_{m}$$":[162],",":[163],"arbitrary":[166],"A0":[168],"rank-1":[170],"matrices":[171],"$$A_{1},":[172],"A_{2},":[173],"\\dots,":[174],"A_{m}$$":[175],".":[176],"also":[179],"viewed":[181],"as":[182],"polynomial":[185],"identity":[186],"corresponding":[191],"determinant":[192],"polynomial.":[193],"Another":[194],"consequence":[195],"solution":[202],"rank":[206],"completion":[208],"Finally,":[210],"we":[211],"representation":[219],"union":[222]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
