{"id":"https://openalex.org/W2780141961","doi":"https://doi.org/10.1007/s00224-018-09908-6","title":"Space-Efficient Algorithms for Longest Increasing Subsequence","display_name":"Space-Efficient Algorithms for Longest Increasing Subsequence","publication_year":2019,"publication_date":"2019-01-22","ids":{"openalex":"https://openalex.org/W2780141961","doi":"https://doi.org/10.1007/s00224-018-09908-6","mag":"2780141961"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-018-09908-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-018-09908-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.09230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041328935","display_name":"Masashi Kiyomi","orcid":"https://orcid.org/0000-0003-1618-9373"},"institutions":[{"id":"https://openalex.org/I89630735","display_name":"Yokohama City University","ror":"https://ror.org/0135d1r83","country_code":"JP","type":"education","lineage":["https://openalex.org/I89630735"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masashi Kiyomi","raw_affiliation_strings":["Yokohama City University, Yokohama, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yokohama City University, Yokohama, Japan","institution_ids":["https://openalex.org/I89630735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045038367","display_name":"Hirotaka Ono","orcid":"https://orcid.org/0000-0003-0845-3947"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hirotaka Ono","raw_affiliation_strings":["Nagoya University, Nagoya, Japan","[Nagoya University, Nagoya, Japan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nagoya University, Nagoya, Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"[Nagoya University, Nagoya, Japan]","institution_ids":["https://openalex.org/I60134161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033878501","display_name":"Yota Otachi","orcid":"https://orcid.org/0000-0002-0087-853X"},"institutions":[{"id":"https://openalex.org/I96036126","display_name":"Kumamoto University","ror":"https://ror.org/02cgss904","country_code":"JP","type":"education","lineage":["https://openalex.org/I96036126"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yota Otachi","raw_affiliation_strings":["Kumamoto University, Kumamoto, Japan","Kumamoto University; Kumamoto Japan"],"raw_orcid":"https://orcid.org/0000-0002-0087-853X","affiliations":[{"raw_affiliation_string":"Kumamoto University, Kumamoto, Japan","institution_ids":["https://openalex.org/I96036126"]},{"raw_affiliation_string":"Kumamoto University; Kumamoto Japan","institution_ids":["https://openalex.org/I96036126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017685495","display_name":"Pascal Schweitzer","orcid":"https://orcid.org/0009-0001-3585-8213"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pascal Schweitzer","raw_affiliation_strings":["TU Kaiserslautern, Kaiserslautern, Germany","TU Kaiserslautern, Kaiserslautern Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"TU Kaiserslautern, Kaiserslautern Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072558440","display_name":"Jun Tarui","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jun Tarui","raw_affiliation_strings":["The University of Electro-Communications, Chofu, Japan","The University of Electro\u2010Communications  Chofu Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Electro-Communications, Chofu, Japan","institution_ids":["https://openalex.org/I20529979"]},{"raw_affiliation_string":"The University of Electro\u2010Communications  Chofu Japan","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5033878501"],"corresponding_institution_ids":["https://openalex.org/I96036126"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.1584,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58656919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"64","issue":"3","first_page":"522","last_page":"541"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9988999962806702,"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/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/subsequence","display_name":"Subsequence","score":0.9412442445755005},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.846701979637146},{"id":"https://openalex.org/keywords/longest-common-subsequence-problem","display_name":"Longest common subsequence problem","score":0.7538857460021973},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7023307085037231},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6707133650779724},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5698860883712769},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5658301711082458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5531924962997437},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4660692512989044},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45952942967414856},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3443681001663208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22034752368927002},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0575927197933197},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04861629009246826}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.9412442445755005},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.846701979637146},{"id":"https://openalex.org/C120098539","wikidata":"https://www.wikidata.org/wiki/Q141001","display_name":"Longest common subsequence problem","level":2,"score":0.7538857460021973},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7023307085037231},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6707133650779724},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5698860883712769},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5658301711082458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5531924962997437},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4660692512989044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45952942967414856},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3443681001663208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22034752368927002},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0575927197933197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04861629009246826},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s00224-018-09908-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-018-09908-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1712.09230","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.09230","pdf_url":"https://arxiv.org/pdf/1712.09230","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:drops-oai.dagstuhl.de:8491","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.44","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol096-stacs2018/LIPIcs.STACS.2018.44/LIPIcs.STACS.2018.44.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"mag:2780141961","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1712.09230v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1712.09230","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.09230","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},{"id":"doi:10.4230/lipics.stacs.2018.44","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.stacs.2018.44","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"mag:2964011774","is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/opus/volltexte/2018/8491/pdf/LIPIcs-STACS-2018-44.pdf/","pdf_url":null,"source":{"id":"https://openalex.org/S4306421002","display_name":"Symposium on Theoretical Aspects of Computer Science","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Symposium on Theoretical Aspects of Computer Science","raw_type":null},{"id":"mag:2997691285","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20180305C126/eng/","pdf_url":null,"source":{"id":"https://openalex.org/S4306512848","display_name":"IEICE Technical Report; IEICE Tech. Rep.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEICE Technical Report; IEICE Tech. Rep.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.09230","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.09230","pdf_url":"https://arxiv.org/pdf/1712.09230","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":0.6299999952316284,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1213650592","display_name":"Theory of Parameterized Complexity for Local Search-Type Computation","funder_award_id":"17H01698","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G284590532","display_name":null,"funder_award_id":"JP18K11168","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3111321927","display_name":"Speeding up FPT algorithms with special tree decompositions","funder_award_id":"18K11168","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3552538742","display_name":null,"funder_award_id":"24106004","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5044127478","display_name":null,"funder_award_id":"24106004","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G5218386026","display_name":null,"funder_award_id":"JP17H01698","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5228531841","display_name":"General algorithms for fixed-parameter intractable problems","funder_award_id":"18K11169","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7407599136","display_name":null,"funder_award_id":"JP24106004","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G8458087533","display_name":null,"funder_award_id":"JP18H04091","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8509000757","display_name":null,"funder_award_id":"JP18K11169","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W615530220","https://openalex.org/W1704788265","https://openalex.org/W1889754528","https://openalex.org/W1976463987","https://openalex.org/W1982129592","https://openalex.org/W1983266860","https://openalex.org/W2001552595","https://openalex.org/W2006656002","https://openalex.org/W2009853785","https://openalex.org/W2014678176","https://openalex.org/W2018407082","https://openalex.org/W2018543684","https://openalex.org/W2027506564","https://openalex.org/W2053984076","https://openalex.org/W2065937173","https://openalex.org/W2066885472","https://openalex.org/W2069893028","https://openalex.org/W2078427855","https://openalex.org/W2081926325","https://openalex.org/W2090968858","https://openalex.org/W2104592606","https://openalex.org/W2105448807","https://openalex.org/W2165056173","https://openalex.org/W2254772976","https://openalex.org/W2265361611","https://openalex.org/W2284006119","https://openalex.org/W2293097972","https://openalex.org/W2400482671","https://openalex.org/W2540137001","https://openalex.org/W2606114621","https://openalex.org/W2729633485","https://openalex.org/W2731520687","https://openalex.org/W2945534310","https://openalex.org/W2952737961","https://openalex.org/W2963401228","https://openalex.org/W4206470441","https://openalex.org/W4235936977","https://openalex.org/W4239639755","https://openalex.org/W4255366398","https://openalex.org/W4299910743","https://openalex.org/W6603257565"],"related_works":["https://openalex.org/W1526908311","https://openalex.org/W149967810","https://openalex.org/W2951206720","https://openalex.org/W2148219949","https://openalex.org/W2950165268","https://openalex.org/W2022086557","https://openalex.org/W2196544305","https://openalex.org/W1518516024","https://openalex.org/W2774400230","https://openalex.org/W2992801300","https://openalex.org/W1876661458","https://openalex.org/W2076406733","https://openalex.org/W16541537","https://openalex.org/W1504152872","https://openalex.org/W1992869351","https://openalex.org/W2477631381","https://openalex.org/W2102347446","https://openalex.org/W2065231486","https://openalex.org/W2042373356","https://openalex.org/W3154370415"],"abstract_inverted_index":{"Given":[0],"a":[1,9,86],"sequence":[2],"of":[3,13,85,114,126,134],"integers,":[4],"we":[5,59],"want":[6],"to":[7,40,120],"find":[8],"longest":[10,87],"increasing":[11,88],"subsequence":[12],"the":[14,42,47,83,111,124,131],"sequence.":[15],"It":[16],"is":[17,39,117],"known":[18],"that":[19,62,110],"this":[20,37],"problem":[21],"can":[22],"be":[23],"solved":[24],"in":[25,36,123],"\\(O\\left":[26,64,71,91],"(n":[27],"\\log":[28,66,77,97],"n\\right":[29,67,78,99],")\\)":[30,68,79,100],"time":[31,48,80,101,112],"and":[32,70,90],"space.":[33,135],"Our":[34],"goal":[35],"paper":[38],"reduce":[41],"space":[43],"consumption":[44],"while":[45],"keeping":[46],"complexity":[49,113],"small.":[50],"For":[51],"\\(\\sqrt":[52],"{n}":[53],"\\le":[54,56],"s":[55],"n\\)":[57],",":[58],"present":[60],"algorithms":[61,116,129],"use":[63],"(s":[65],"bits":[69],"(\\frac":[72,92],"{1}{s}":[73,93],"\\cdot":[74,76,94,96],"n^{2}":[75,95],"for":[81,102],"computing":[82],"length":[84],"subsequence,":[89],"^{2}":[98],"finding":[103],"an":[104],"actual":[105],"subsequence.":[106],"We":[107],"also":[108],"show":[109],"our":[115],"optimal":[118],"up":[119],"polylogarithmic":[121],"factors":[122],"framework":[125],"sequential":[127],"access":[128],"with":[130],"prescribed":[132],"amount":[133]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}