{"id":"https://openalex.org/W2940220397","doi":"https://doi.org/10.1109/tit.2021.3066010","title":"Trace Reconstruction: Generalized and Parameterized","display_name":"Trace Reconstruction: Generalized and Parameterized","publication_year":2021,"publication_date":"2021-03-17","ids":{"openalex":"https://openalex.org/W2940220397","doi":"https://doi.org/10.1109/tit.2021.3066010","mag":"2940220397"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3066010","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3066010","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1904.09618","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015082848","display_name":"Akshay Krishnamurthy","orcid":"https://orcid.org/0000-0002-5738-2383"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4401726785","display_name":"Microsoft Research New York City (United States)","ror":"https://ror.org/056zprp28","country_code":null,"type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4401726785"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Akshay Krishnamurthy","raw_affiliation_strings":["Microsoft Research, New York City, NY, USA","Microsoft Research, New York City, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, New York City, NY, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4401726785"]},{"raw_affiliation_string":"Microsoft Research, New York City, NY, USA#TAB#","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4401726785"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051046818","display_name":"Arya Mazumdar","orcid":"https://orcid.org/0000-0003-4605-7996"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arya Mazumdar","raw_affiliation_strings":["Hal\u0131c\u0131o\u01e7lu Data Science Institute, University of California San Diego, San Diego, CA, USA"],"affiliations":[{"raw_affiliation_string":"Hal\u0131c\u0131o\u01e7lu Data Science Institute, University of California San Diego, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101979548","display_name":"Andrew McGregor","orcid":"https://orcid.org/0000-0002-2124-160X"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew McGregor","raw_affiliation_strings":["College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA","College of Information and Computer Sciences; University of Massachusetts-Amherst; Amherst MA USA"],"affiliations":[{"raw_affiliation_string":"College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]},{"raw_affiliation_string":"College of Information and Computer Sciences; University of Massachusetts-Amherst; Amherst MA USA","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047754690","display_name":"Soumyabrata Pal","orcid":"https://orcid.org/0000-0003-2949-3761"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Soumyabrata Pal","raw_affiliation_strings":["College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA","College of Information and Computer Sciences; University of Massachusetts-Amherst; Amherst MA USA"],"affiliations":[{"raw_affiliation_string":"College of Information and Computer Sciences, University of Massachusetts Amherst, Amherst, MA, USA","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]},{"raw_affiliation_string":"College of Information and Computer Sciences; University of Massachusetts-Amherst; Amherst MA USA","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015082848"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4401726785"],"apc_list":null,"apc_paid":null,"fwci":1.1652,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.79906285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"67","issue":"6","first_page":"3233","last_page":"3250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.696556568145752},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6964813470840454},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6714245080947876},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6080114245414734},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.584071695804596},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5620272159576416},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.551113486289978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5417743921279907},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5236555933952332},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4435422718524933},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4248073995113373},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.41658639907836914},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3936510980129242},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.105471670627594},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08172047138214111}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.696556568145752},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6964813470840454},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6714245080947876},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6080114245414734},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.584071695804596},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5620272159576416},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.551113486289978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5417743921279907},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5236555933952332},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4435422718524933},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4248073995113373},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.41658639907836914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3936510980129242},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.105471670627594},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08172047138214111},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3066010","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3066010","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1904.09618","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.09618","pdf_url":"https://arxiv.org/pdf/1904.09618","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2940220397","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1904.09618.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1904.09618","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.09618","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1904.09618","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.09618","pdf_url":"https://arxiv.org/pdf/1904.09618","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1765714014","display_name":null,"funder_award_id":"CCF1642658","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2158607031","display_name":null,"funder_award_id":"1763618","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2993029871","display_name":null,"funder_award_id":"1908849","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3109196640","display_name":null,"funder_award_id":"1934846","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3385483125","display_name":null,"funder_award_id":"1909046","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8050074586","display_name":null,"funder_award_id":"1637536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1133414672","https://openalex.org/W1574816920","https://openalex.org/W1763164889","https://openalex.org/W1956647075","https://openalex.org/W1967505984","https://openalex.org/W1969015668","https://openalex.org/W1969151232","https://openalex.org/W1971402995","https://openalex.org/W1985792472","https://openalex.org/W2012828271","https://openalex.org/W2025177415","https://openalex.org/W2026302946","https://openalex.org/W2035420487","https://openalex.org/W2058068142","https://openalex.org/W2059420131","https://openalex.org/W2062817469","https://openalex.org/W2063573129","https://openalex.org/W2095554889","https://openalex.org/W2170484108","https://openalex.org/W2177772290","https://openalex.org/W2564763601","https://openalex.org/W2565322834","https://openalex.org/W2939764522","https://openalex.org/W2951177125","https://openalex.org/W2962802724","https://openalex.org/W2962820675","https://openalex.org/W2963134372","https://openalex.org/W2963414662","https://openalex.org/W2964199960","https://openalex.org/W2964371621","https://openalex.org/W2971926581","https://openalex.org/W3028579427","https://openalex.org/W3033084890","https://openalex.org/W4285719527","https://openalex.org/W6656576250","https://openalex.org/W6665204704","https://openalex.org/W6666485203","https://openalex.org/W6747734592","https://openalex.org/W6758833420"],"related_works":["https://openalex.org/W3161798670","https://openalex.org/W2963134372","https://openalex.org/W2564763601","https://openalex.org/W2063573129","https://openalex.org/W2025177415","https://openalex.org/W2020301027","https://openalex.org/W3037885501","https://openalex.org/W3046745563","https://openalex.org/W1556308264","https://openalex.org/W2586408739","https://openalex.org/W1923547365","https://openalex.org/W2051573271","https://openalex.org/W2918767742","https://openalex.org/W2963366490","https://openalex.org/W2971926581","https://openalex.org/W2965187759","https://openalex.org/W2565322834","https://openalex.org/W2170484108","https://openalex.org/W2399534654","https://openalex.org/W2952014918"],"abstract_inverted_index":{"In":[0,86,130],"the":[1,8,47,80,131,135,156,164,197,210,244,278],"beautifully":[2],"simple-to-state":[3],"problem":[4,41,81,97,198],"of":[5,21,32,79,95,134,141,280],"trace":[6,25],"reconstruction,":[7],"goal":[9],"is":[10,26,42,50,55,64,82,146,169,193,204,215,267],"to":[11,101,196,236],"reconstruct":[12,237],"an":[13,66,99,142,241],"unknown":[14,48,143],"binary":[15],"string":[16,49],"x":[17,22,33,266,283],"given":[18],"random":[19,180,200],"\u201ctraces\u201d":[20],"where":[23,163,202],"each":[24,30,137],"generated":[27],"by":[28,286],"deleting":[29],"coordinate":[31],"independently":[34,148],"with":[35,149,155],"probability":[36,150],"p":[37],"<;":[38],"1.":[39],"The":[40],"well":[43],"studied":[44],"both":[45,61],"when":[46,53,250],"arbitrary":[51,128],"and":[52,71,76,93,105,139,190,209,269],"it":[54],"chosen":[56],"uniformly":[57],"at":[58],"random.":[59],"For":[60],"settings,":[62],"there":[63,203],"still":[65,83],"exponential":[67],"gap":[68],"between":[69],"upper":[70,167,213],"lower":[72,207],"sample":[73],"complexity":[74],"bounds":[75],"our":[77,110],"understanding":[78],"surprisingly":[84],"limited.":[85],"this":[87,96],"paper,":[88],"we":[89,183,270],"consider":[90],"natural":[91],"parameterizations":[92],"generalizations":[94],"in":[98,194,282],"effort":[100],"attain":[102],"a":[103,205,273],"deeper":[104],"more":[106],"comprehensive":[107],"understanding.":[108],"Perhaps":[109],"most":[111],"surprising":[112],"results":[113,153,159,249],"are:":[114],"1)":[115],"We":[116,222,259],"prove":[117],"that":[118,185,224,261,277],"exp(O(n":[119,170],"<sup":[120,171,217,226,230,254],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[121,172,218,227,231,255],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1/4</sup>":[122],"\u221a{logn}))":[123],"traces":[124,187,234,263],"suffice":[125,235,264],"for":[126,160,179,199],"reconstructing":[127],"matrices.":[129],"matrix":[132,145,181],"version":[133],"problem,":[136],"row":[138],"column":[140],"\u221an\u00d7\u221an":[144],"deleted":[147],"p.":[151],"Our":[152],"contrasts":[154],"best":[157,165,211,245],"known":[158,166,212,246],"sequence":[161,247],"reconstruction":[162,248],"bound":[168,208,214],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1/3</sup>":[173,219,228],")).":[174],"2)":[175],"An":[176],"optimal":[177],"result":[178],"reconstruction:":[182],"show":[184,223,260],"\u0398(logn)":[186],"are":[188],"necessary":[189],"sufficient.":[191],"This":[192],"contrast":[195],"sequences":[201],"super-logarithmic":[206],"exp(O(log":[216],"n)).":[220],"3)":[221],"exp(O(k":[225],"log":[229],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2/3</sup>":[232],"n))":[233],"k-sparse":[238,268],"strings,":[239],"providing":[240],"improvement":[242],"over":[243],"k":[251],"=":[252],"o(n/log":[253],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[256],"n).":[257],"4)":[258],"poly(n)":[262],"if":[265],"additionally":[271],"have":[272],"\u201cseparation\u201d":[274],"promise,":[275],"specifically":[276],"indices":[279],"1's":[281],"all":[284],"differ":[285],"\u03a9(k":[287],"logn).":[288]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}