{"id":"https://openalex.org/W2802074115","doi":"https://doi.org/10.1137/17m112258x","title":"Matrix Rigidity from the Viewpoint of Parameterized Complexity","display_name":"Matrix Rigidity from the Viewpoint of Parameterized Complexity","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2802074115","doi":"https://doi.org/10.1137/17m112258x","mag":"2802074115"},"language":"en","primary_location":{"id":"doi:10.1137/17m112258x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m112258x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5075328697","display_name":"Fedor V. Fomin","orcid":"https://orcid.org/0000-0003-1955-4612"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fedor V. Fomin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038531405","display_name":"Daniel Lokshtanov","orcid":"https://orcid.org/0000-0002-3166-9212"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056943131","display_name":"Syed Mohammad Meesum","orcid":"https://orcid.org/0000-0002-1771-403X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. M. Meesum","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082025487","display_name":"Meirav Zehavi","orcid":"https://orcid.org/0000-0002-3636-5322"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meirav Zehavi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6181,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70163791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"32","issue":"2","first_page":"966","last_page":"985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.9122912287712097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7286031246185303},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.7269014120101929},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.491676390171051},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48424169421195984},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4688993990421295},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4686030149459839},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4607800543308258},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4580795168876648},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3283098638057709},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2094871997833252},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07912400364875793}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.9122912287712097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7286031246185303},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.7269014120101929},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.491676390171051},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48424169421195984},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4688993990421295},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4686030149459839},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4607800543308258},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4580795168876648},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3283098638057709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2094871997833252},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07912400364875793},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m112258x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m112258x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7417038317","display_name":null,"funder_award_id":"306992","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1626181984","https://openalex.org/W1991813962","https://openalex.org/W2008671178","https://openalex.org/W2053068069","https://openalex.org/W2061133474","https://openalex.org/W2064269488","https://openalex.org/W2119106791","https://openalex.org/W2137442467"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2360897844","https://openalex.org/W2171811389","https://openalex.org/W2041837101","https://openalex.org/W1598441350","https://openalex.org/W1539117866"],"abstract_inverted_index":{"For":[0],"a":[1,8,12,23,32,77,89,162,169,198,222,227,232],"target":[2,128],"rank":[3,26,129],"$r$,":[4],"the":[5,16,58,63,74,96,99,105,116,122,127,139,205,239],"rigidity":[6,75,100,123],"of":[7,25,40,49,60,65,68,73,76,92,95,98,101,107,124,175,177,207,235,242],"matrix":[9,24,78],"$A$":[10,21,125],"over":[11],"field":[13],"$\\mathbb{F}$":[14,143],"is":[15,31,131,144,150],"minimum":[17],"Hamming":[18],"distance":[19],"between":[20],"and":[22,72,114,226],"at":[27,132],"most":[28,133],"$r$.":[29],"Rigidity":[30,118],"classical":[33],"concept":[34],"in":[35,70,79,104,138,172,185,194],"computational":[36],"complexity":[37],"theory:":[38],"constructions":[39],"rigid":[41],"matrices":[42,69,103],"are":[43,190,219],"known":[44,193],"to":[45,53,155],"imply":[46],"lower":[47],"bounds":[48],"significant":[50],"importance":[51],"relating":[52],"arithmetic":[54],"circuits.":[55],"Yet,":[56],"from":[57],"viewpoint":[59],"parameterized":[61,108,195,229],"complexity,":[62,196],"study":[64,91],"central":[66,183],"properties":[67],"general,":[71],"particular,":[80,202],"has":[81],"been":[82],"neglected.":[83],"In":[84,201],"this":[85,148,158,178,243],"paper,":[86],"we":[87,160,203],"conduct":[88],"comprehensive":[90],"different":[93,240],"aspects":[94],"computation":[97],"general":[102],"framework":[106],"complexity.":[109],"Naturally,":[110],"given":[111],"parameters":[112],"$r$":[113,130],"$k$,":[115],"Matrix":[117,236],"problem":[119,149],"asks":[120],"whether":[121],"for":[126,231],"$k$.":[134],"We":[135,180],"show":[136],"that":[137],"case":[140,234],"$\\mathbb{F}=\\mathbb{R}$":[141],"or":[142],"any":[145],"finite":[146],"field,":[147],"fixed-parameter":[151],"tractable":[152],"with":[153],"respect":[154],"$k+r$.":[156],"To":[157],"end,":[159],"present":[161],"dimension":[163,209],"reduction":[164,210],"procedure,":[165],"which":[166,189],"may":[167],"be":[168],"valuable":[170],"primitive":[171],"future":[173],"studies":[174],"problems":[176],"nature.":[179],"also":[181],"employ":[182],"tools":[184],"real":[186],"algebraic":[187,214],"geometry,":[188],"not":[191],"well":[192],"as":[197,212],"black":[199],"box.":[200],"view":[204],"output":[206],"our":[208],"procedure":[211],"an":[213],"variety.":[215],"Our":[216],"main":[217],"results":[218],"complemented":[220],"by":[221],"\\sf":[223],"W[1]-hardness":[224],"result":[225],"subexponential-time":[228],"algorithm":[230],"special":[233],"Rigidity,":[237],"highlighting":[238],"flavors":[241],"problem.":[244]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}