{"id":"https://openalex.org/W4289655407","doi":"https://doi.org/10.1109/isit50566.2022.9834537","title":"The Gapped k-Deck Problem","display_name":"The Gapped k-Deck Problem","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4289655407","doi":"https://doi.org/10.1109/isit50566.2022.9834537"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834537","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5079697219","display_name":"Rebecca Golm","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jonas Golm","raw_affiliation_strings":["University of Illinois,ECE Department","ECE Department, University of Illinois"],"affiliations":[{"raw_affiliation_string":"University of Illinois,ECE Department","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"ECE Department, University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019755068","display_name":"Mina Nahvi","orcid":"https://orcid.org/0000-0002-0865-395X"},"institutions":[{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I16820183","display_name":"Illinois College","ror":"https://ror.org/02ys5x139","country_code":"US","type":"education","lineage":["https://openalex.org/I16820183"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mina Nahvi","raw_affiliation_strings":["University of Illinois,Department of Mathematics","Department of Mathematics, University of Illinois"],"affiliations":[{"raw_affiliation_string":"University of Illinois,Department of Mathematics","institution_ids":["https://openalex.org/I16820183","https://openalex.org/I2801919071","https://openalex.org/I39422238"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008430584","display_name":"Ryan Gabrys","orcid":"https://orcid.org/0000-0002-9197-3371"},"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":"Ryan Gabrys","raw_affiliation_strings":["University of California,Calit2,San Diego","Calit2, University of California, San Diego"],"affiliations":[{"raw_affiliation_string":"University of California,Calit2,San Diego","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Calit2, University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084947882","display_name":"Olgica Milenkovi\u0107","orcid":"https://orcid.org/0000-0002-1871-4912"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olgica Milenkovic","raw_affiliation_strings":["University of Illinois,ECE Department","ECE Department, University of Illinois"],"affiliations":[{"raw_affiliation_string":"University of Illinois,ECE Department","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"ECE Department, University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079697219"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.5194,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62685844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"49","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9995999932289124,"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":0.9995999932289124,"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":0.995199978351593,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9896000027656555,"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/multiset","display_name":"Multiset","score":0.7401965260505676},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6182311177253723},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6088061928749084},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5743138790130615},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5229161977767944},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4713665246963501},{"id":"https://openalex.org/keywords/deck","display_name":"Deck","score":0.4580570161342621},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4514249861240387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44207966327667236},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.374640554189682},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35333386063575745}],"concepts":[{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.7401965260505676},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6182311177253723},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6088061928749084},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5743138790130615},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5229161977767944},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4713665246963501},{"id":"https://openalex.org/C2778966251","wikidata":"https://www.wikidata.org/wiki/Q208123","display_name":"Deck","level":2,"score":0.4580570161342621},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4514249861240387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44207966327667236},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.374640554189682},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35333386063575745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834537","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1574079735","https://openalex.org/W2014342457","https://openalex.org/W2016219933","https://openalex.org/W2025177415","https://openalex.org/W2031816626","https://openalex.org/W2097130855","https://openalex.org/W2336019055","https://openalex.org/W2584062640","https://openalex.org/W2912739023","https://openalex.org/W2951269465","https://openalex.org/W2963412269","https://openalex.org/W2969308577","https://openalex.org/W2989916841","https://openalex.org/W3028579427","https://openalex.org/W3169706614","https://openalex.org/W6656576250"],"related_works":["https://openalex.org/W2314929580","https://openalex.org/W2129688665","https://openalex.org/W2091042571","https://openalex.org/W2393028428","https://openalex.org/W2973235923","https://openalex.org/W2105467293","https://openalex.org/W4251905599","https://openalex.org/W1815571","https://openalex.org/W2156516305","https://openalex.org/W2502624504"],"abstract_inverted_index":{"The":[0,89],"k-deck":[1,43,125],"problem":[2,40],"is":[3],"concerned":[4],"with":[5],"finding":[6],"the":[7,25,29,38,53,93,96,106,122,131,139,158],"smallest":[8,54],"positive":[9,55],"integer":[10,56],"S(k)":[11,22],"such":[12,62],"that":[13,23,63,78],"there":[14,64],"exist":[15,65],"at":[16,66,100],"least":[17,67,101],"two":[18,68],"strings":[19,70],"of":[20,31,33,41,71,87,130],"length":[21,34,72],"share":[24],"same":[26,123],"k-deck,":[27],"i.e.,":[28],"multiset":[30],"subsequences":[32,97],"k.":[35],"We":[36],"introduce":[37],"new":[39],"gapped":[42],"reconstruction:":[44],"For":[45],"a":[46,84,127],"given":[47],"gap":[48,90],"parameter":[49],"s,":[50],"we":[51,115,152],"seek":[52],"G":[57,73,146],"<inf":[58,74,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[59,75,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</inf>":[60,76],"(k)":[61,77],"distinct":[69],"cannot":[79],"be":[80,99],"distinguished":[81],"based":[82],"on":[83,145],"\"gapped\"":[85],"set":[86],"k-subsequences.":[88],"constraint":[91],"requires":[92],"elements":[94],"in":[95],"to":[98,118],"s":[102],"positions":[103],"apart":[104],"within":[105],"original":[107],"string.":[108],"Our":[109],"results":[110],"are":[111],"as":[112],"follows.":[113],"First,":[114],"show":[116],"how":[117],"construct":[119],"sequences":[120],"sharing":[121],"2-gapped":[124],"using":[126,157],"nontrivial":[128],"modification":[129],"recursive":[132],"Morse-Thue":[133],"string":[134],"construction":[135],"procedure.":[136],"This":[137],"establishes":[138],"first":[140],"known":[141],"constructive":[142],"upper":[143],"bound":[144,156],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[149],"(k).":[150],"Second,":[151],"further":[153],"improve":[154],"this":[155],"approach":[159],"by":[160],"Dudik":[161],"and":[162],"Schulman":[163],"[6].":[164]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-08-03T00:00:00"}