{"id":"https://openalex.org/W2091419774","doi":"https://doi.org/10.1145/1516512.1516519","title":"Improved bounds on the average length of longest common subsequences","display_name":"Improved bounds on the average length of longest common subsequences","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2091419774","doi":"https://doi.org/10.1145/1516512.1516519","mag":"2091419774"},"language":"en","primary_location":{"id":"doi:10.1145/1516512.1516519","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1516512.1516519","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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/A5079864020","display_name":"George S. Lueker","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George S. Lueker","raw_affiliation_strings":["University of California, Irvine, California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine, California","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079864020"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":null,"apc_paid":null,"fwci":4.5275,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.94616127,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"56","issue":"3","first_page":"1","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9965000152587891,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.8296130895614624},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8213028907775879},{"id":"https://openalex.org/keywords/longest-common-subsequence-problem","display_name":"Longest common subsequence problem","score":0.7235090732574463},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6736599802970886},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6419817209243774},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6333008408546448},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.602840006351471},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5914202332496643},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5188054442405701},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.4874989986419678},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4590100646018982},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3356306552886963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1748799979686737},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13458716869354248},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.061864763498306274}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8296130895614624},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8213028907775879},{"id":"https://openalex.org/C120098539","wikidata":"https://www.wikidata.org/wiki/Q141001","display_name":"Longest common subsequence problem","level":2,"score":0.7235090732574463},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6736599802970886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6419817209243774},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6333008408546448},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.602840006351471},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5914202332496643},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5188054442405701},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.4874989986419678},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4590100646018982},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3356306552886963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1748799979686737},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13458716869354248},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.061864763498306274},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1516512.1516519","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1516512.1516519","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W194677851","https://openalex.org/W1490430289","https://openalex.org/W1533404702","https://openalex.org/W1551519020","https://openalex.org/W1606584921","https://openalex.org/W1948141881","https://openalex.org/W1988684690","https://openalex.org/W1990144193","https://openalex.org/W1991983464","https://openalex.org/W1992904575","https://openalex.org/W2002883296","https://openalex.org/W2010260400","https://openalex.org/W2019211725","https://openalex.org/W2093217046","https://openalex.org/W2099591940","https://openalex.org/W2162744351","https://openalex.org/W2165341195","https://openalex.org/W2165469059","https://openalex.org/W2295428206","https://openalex.org/W2478722229","https://openalex.org/W2970618185","https://openalex.org/W3103549653","https://openalex.org/W3144881883","https://openalex.org/W4231916799"],"related_works":["https://openalex.org/W4225868058","https://openalex.org/W3022573534","https://openalex.org/W2152064395","https://openalex.org/W4289596129","https://openalex.org/W1540010783","https://openalex.org/W3083981518","https://openalex.org/W3094761360","https://openalex.org/W25732909","https://openalex.org/W3013933387","https://openalex.org/W1974063126"],"abstract_inverted_index":{"It":[0],"has":[1],"long":[2],"been":[3],"known":[4],"[Chv\u00e1tal":[5],"and":[6,53,61,80,93,103,107,112,120],"Sankoff":[7],"1975]":[8],"that":[9,141,158,168],"the":[10,14,89,128,169,195],"average":[11],"length":[12,23],"of":[13,18,22,28,48,56,101,186],"longest":[15],"common":[16],"subsequence":[17],"two":[19],"random":[20],"strings":[21],"n":[24,36],"over":[25],"an":[26],"alphabet":[27],"size":[29],"k":[30,35,41,44,182,192],"is":[31,125],"asymptotic":[32],"to":[33,118,178,190],"\u03b3":[34,40,97,129,142,191],"for":[37,77,96,180],"some":[38],"constant":[39],"depending":[42],"on":[43,64,74,83],".":[45],"The":[46],"value":[47,161],"these":[49,84,117],"constants":[50],"remains":[51],"unknown,":[52],"a":[54,184],"number":[55],"papers":[57],"have":[58],"proved":[59],"upper":[60,81,94,123,170,187],"lower":[62,79,92],"bounds":[63,82,95,188,203],"them.":[65],"We":[66,115],"discuss":[67],"techniques,":[68],"involving":[69],"numerical":[70],"calculations":[71],"with":[72],"recurrences":[73],"many":[75],"variables,":[76],"determining":[78],"constants.":[85],"To":[86],"our":[87],"knowledge,":[88],"previous":[90],"best-known":[91],"2":[98,130,143],"were":[99],"those":[100],"Dan\u010d\u00edk":[102,111],"Paterson,":[104],"approximately":[105],"0.773911":[106],"0.837623":[108],"[Dan\u010d\u00edk":[109],"1994;":[110],"Paterson":[113],"1995].":[114],"improve":[116],"0.788071":[119],"0.826280.":[121],"This":[122],"bound":[124,171],"less":[126],"than":[127],"given":[131],"by":[132],"Steele's":[133],"old":[134],"conjecture":[135],"(see":[136],"Steele":[137,150],"[1997,":[138],"page":[139],"3])":[140],"=":[144],"2/(1":[145],"+":[146],"\u221a2)\u2248":[147],"0.828427.":[148],"(As":[149],"points":[151],"out,":[152],"experimental":[153],"evidence":[154],"had":[155],"already":[156],"suggested":[157],"this":[159],"conjectured":[160],"was":[162],"too":[163],"high.)":[164],"Finally,":[165],"we":[166],"show":[167],"technique":[172],"described":[173],"here":[174],"could":[175],"be":[176],"used":[177],"produce,":[179],"any":[181],",":[183,193],"sequence":[185],"converging":[189],"though":[194],"computation":[196],"time":[197],"grows":[198],"very":[199],"quickly":[200],"as":[201],"better":[202],"are":[204],"guaranteed.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}