{"id":"https://openalex.org/W2968548673","doi":"https://doi.org/10.1109/tit.2020.3038147","title":"The Smallest Grammar Problem Revisited","display_name":"The Smallest Grammar Problem Revisited","publication_year":2020,"publication_date":"2020-11-13","ids":{"openalex":"https://openalex.org/W2968548673","doi":"https://doi.org/10.1109/tit.2020.3038147","mag":"2968548673"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2020.3038147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3038147","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/1908.06428","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011046118","display_name":"Hideo Bannai","orcid":"https://orcid.org/0000-0002-6856-5185"},"institutions":[{"id":"https://openalex.org/I125602781","display_name":"Tokyo Medical and Dental University","ror":"https://ror.org/051k3eh31","country_code":"JP","type":"education","lineage":["https://openalex.org/I125602781"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hideo Bannai","raw_affiliation_strings":["Tokyo Medical and Dental University, Tokyo, Japan","Department of Data Science Algorithm Design and Analysis, Tokyo Medical and Dental University, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo Medical and Dental University, Tokyo, Japan","institution_ids":["https://openalex.org/I125602781"]},{"raw_affiliation_string":"Department of Data Science Algorithm Design and Analysis, Tokyo Medical and Dental University, Tokyo, Japan","institution_ids":["https://openalex.org/I125602781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004337463","display_name":"Momoko Hirayama","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Momoko Hirayama","raw_affiliation_strings":["Kyushu University, Fukuoka, Japan","[Dept. of Informatics, Kyushu University, Fukuoka, Japan]"],"affiliations":[{"raw_affiliation_string":"Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"[Dept. of Informatics, Kyushu University, Fukuoka, Japan]","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032713735","display_name":"Danny Hucke","orcid":null},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Danny Hucke","raw_affiliation_strings":["University of Siegen, Siegen, Germany","[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012002493","display_name":"Shunsuke Inenaga","orcid":"https://orcid.org/0000-0002-1833-010X"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shunsuke Inenaga","raw_affiliation_strings":["Kyushu University, Fukuoka, Japan","[Dept. of Informatics, Kyushu University, Fukuoka, Japan]"],"affiliations":[{"raw_affiliation_string":"Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"[Dept. of Informatics, Kyushu University, Fukuoka, Japan]","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066525178","display_name":"Artur Je\u017c","orcid":"https://orcid.org/0000-0003-4321-3105"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Artur Jez","raw_affiliation_strings":["Institute of Computer Science, University of Wroc\u0142aw, Wroc\u0142aw, Poland","[Inst. of Comput. Sci., Univ. of Wroclaw, Wroc\u0142aw, Poland]"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"[Inst. of Comput. Sci., Univ. of Wroclaw, Wroc\u0142aw, Poland]","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Lohrey","raw_affiliation_strings":["University of Siegen, Siegen, Germany","[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018429583","display_name":"Carl Philipp Reh","orcid":"https://orcid.org/0000-0002-3884-8942"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Carl Philipp Reh","raw_affiliation_strings":["University of Siegen, Siegen, Germany","[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"[Department of Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany]","institution_ids":["https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5011046118"],"corresponding_institution_ids":["https://openalex.org/I125602781"],"apc_list":null,"apc_paid":null,"fwci":0.2937191,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60672316,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"1","first_page":"317","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"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/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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/T12029","display_name":"DNA and Biological Computing","score":0.9988999962806702,"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/omega","display_name":"Omega","score":0.7626680135726929},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7476297616958618},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7041984796524048},{"id":"https://openalex.org/keywords/grammar","display_name":"Grammar","score":0.47697171568870544},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4707746207714081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4360724687576294},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37509334087371826},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1352159082889557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08475601673126221},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.053681880235672}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7626680135726929},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7476297616958618},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7041984796524048},{"id":"https://openalex.org/C26022165","wikidata":"https://www.wikidata.org/wiki/Q8091","display_name":"Grammar","level":2,"score":0.47697171568870544},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4707746207714081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4360724687576294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37509334087371826},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1352159082889557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08475601673126221},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.053681880235672},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2020.3038147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3038147","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:1908.06428","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.06428","pdf_url":"https://arxiv.org/pdf/1908.06428","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:2968548673","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.06428.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.1908.06428","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1908.06428","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:1908.06428","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.06428","pdf_url":"https://arxiv.org/pdf/1908.06428","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":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2968548673.pdf","grobid_xml":"https://content.openalex.org/works/W2968548673.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W327921858","https://openalex.org/W589745946","https://openalex.org/W1484484268","https://openalex.org/W1529451410","https://openalex.org/W1532033082","https://openalex.org/W1973608346","https://openalex.org/W1976149088","https://openalex.org/W2022126655","https://openalex.org/W2028460486","https://openalex.org/W2037818726","https://openalex.org/W2041211107","https://openalex.org/W2052653988","https://openalex.org/W2062429446","https://openalex.org/W2105686649","https://openalex.org/W2111487449","https://openalex.org/W2113004376","https://openalex.org/W2119924552","https://openalex.org/W2122962290","https://openalex.org/W2130433404","https://openalex.org/W2130956967","https://openalex.org/W2132809979","https://openalex.org/W2147344024","https://openalex.org/W2150056094","https://openalex.org/W2150663494","https://openalex.org/W2171532727","https://openalex.org/W2171818384","https://openalex.org/W2321308325","https://openalex.org/W2522260339","https://openalex.org/W2538584224","https://openalex.org/W2567634998","https://openalex.org/W2592570088","https://openalex.org/W2612743067","https://openalex.org/W2765521106","https://openalex.org/W2799020565","https://openalex.org/W2890245531","https://openalex.org/W2900135494","https://openalex.org/W2952265035","https://openalex.org/W2955987721","https://openalex.org/W2964215495","https://openalex.org/W2979888527","https://openalex.org/W4245857357","https://openalex.org/W6617424981","https://openalex.org/W6675130072","https://openalex.org/W6729180420","https://openalex.org/W6775842624"],"related_works":["https://openalex.org/W2951844571","https://openalex.org/W2502975660","https://openalex.org/W844866297","https://openalex.org/W1550265671","https://openalex.org/W1510886914","https://openalex.org/W3101998289","https://openalex.org/W2885668447","https://openalex.org/W2166853092","https://openalex.org/W2041493135","https://openalex.org/W3209482599","https://openalex.org/W2950284340","https://openalex.org/W2287138463","https://openalex.org/W3101125945","https://openalex.org/W2963892825","https://openalex.org/W3118917224","https://openalex.org/W2949921088","https://openalex.org/W3101386124","https://openalex.org/W2963003754","https://openalex.org/W3012317967","https://openalex.org/W2993582139"],"abstract_inverted_index":{"In":[0,72],"a":[1,34],"seminal":[2],"paper":[3],"of":[4,57,67,90],"Charikar":[5],"et":[6],"al.":[7],"on":[8,20],"the":[9,13,21,37,43,54,64,74],"smallest":[10],"grammar":[11],"problem,":[12],"authors":[14],"derive":[15],"upper":[16,40],"and":[17,39,47,92,100],"lower":[18,38,75],"bounds":[19],"approximation":[22,55,65],"ratios":[23],"for":[24,45,77,97],"several":[25],"grammar-based":[26,95],"compressors,":[27],"but":[28],"in":[29],"all":[30],"cases":[31],"there":[32],"is":[33,59,69,79],"gap":[35],"between":[36],"bound.":[41],"Here":[42],"gaps":[44],"$\\mathsf{LZ78}$":[46,58],"$\\mathsf{BISECTION}$":[48,68],"are":[49,103],"closed":[50],"by":[51],"showing":[52],"that":[53],"ratio":[56,66],"$\u0398(":[60],"(n/\\log":[61],"n)^{2/3})$,":[62],"whereas":[63],"$\u0398(\\sqrt{n/\\log":[70],"n})$.":[71],"addition,":[73],"bound":[76],"$\\mathsf{RePair}$":[78],"improved":[80],"from":[81],"$\u03a9(\\sqrt{\\log":[82],"n})$":[83],"to":[84],"$\u03a9(\\log":[85],"n/\\log\\log":[86],"n)$.":[87],"Finally,":[88],"results":[89],"Arpe":[91],"Reischuk":[93],"relating":[94],"compression":[96],"arbitrary":[98],"alphabets":[99,102],"binary":[101],"improved.":[104]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}