{"id":"https://openalex.org/W2145381651","doi":"https://doi.org/10.1007/s00453-014-9915-3","title":"Fast Algorithm for Partial Covers in Words","display_name":"Fast Algorithm for Partial Covers in Words","publication_year":2014,"publication_date":"2014-07-15","ids":{"openalex":"https://openalex.org/W2145381651","doi":"https://doi.org/10.1007/s00453-014-9915-3","mag":"2145381651"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-014-9915-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9915-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9915-3.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9915-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086467798","display_name":"Tomasz Kociumaka","orcid":"https://orcid.org/0000-0002-2477-1702"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tomasz Kociumaka","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051275317","display_name":"Solon P. Pissis","orcid":"https://orcid.org/0000-0002-1445-1932"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Solon P. Pissis","raw_affiliation_strings":["Department of Informatics, King\u2019s College London, London\u00a0, WC2R 2LS, UK","Department of Informatics, King's College London, London\u00a0, WC2R 2LS, UK"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, King\u2019s College London, London\u00a0, WC2R 2LS, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"Department of Informatics, King's College London, London\u00a0, WC2R 2LS, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082711976","display_name":"Jakub Radoszewski","orcid":"https://orcid.org/0000-0002-0067-6401"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Radoszewski","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079957387","display_name":"Wojciech Rytter","orcid":"https://orcid.org/0000-0002-9162-6724"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Wojciech Rytter","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Copernicus University, Toru\u0144, Poland","Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Copernicus University, Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]},{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061843884","display_name":"Tomasz Wale\u0144","orcid":"https://orcid.org/0000-0002-7369-3309"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tomasz Wale\u0144","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5086467798"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.2721,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.85855085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"73","issue":"1","first_page":"217","last_page":"233"},"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/T11567","display_name":"semigroups and automata theory","score":0.9959999918937683,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/cover","display_name":"Cover (algebra)","score":0.8116805553436279},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7288093566894531},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6000162363052368},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5714207291603088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5397613048553467},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4467325508594513},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4396378695964813},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.41471365094184875},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4127293825149536},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10664668679237366}],"concepts":[{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.8116805553436279},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7288093566894531},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6000162363052368},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5714207291603088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5397613048553467},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4467325508594513},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4396378695964813},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.41471365094184875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4127293825149536},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10664668679237366},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00453-014-9915-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9915-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9915-3.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:openaire/59911d20-ca38-4d05-93c0-9b0db504c793","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/59911d20-ca38-4d05-93c0-9b0db504c793","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kociumaka, T, Pissis, S P, Radoszewski, J, Rytter, W & Walen, T 2015, 'Fast Algorithm for Partial Covers in Words', ALGORITHMICA, vol. 73, no. 1, pp. 217-233. https://doi.org/10.1007/s00453-014-9915-3","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00453-014-9915-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9915-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9915-3.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2145381651.pdf","grobid_xml":"https://content.openalex.org/works/W2145381651.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W63662079","https://openalex.org/W162684057","https://openalex.org/W204059611","https://openalex.org/W642038236","https://openalex.org/W1495524224","https://openalex.org/W1496038746","https://openalex.org/W1504417041","https://openalex.org/W1513386425","https://openalex.org/W1515213620","https://openalex.org/W1882010690","https://openalex.org/W1967382114","https://openalex.org/W1992151876","https://openalex.org/W1995705893","https://openalex.org/W2020590137","https://openalex.org/W2036042874","https://openalex.org/W2051593658","https://openalex.org/W2056819372","https://openalex.org/W2056972845","https://openalex.org/W2059513841","https://openalex.org/W2065209187","https://openalex.org/W2066797099","https://openalex.org/W2084345246","https://openalex.org/W2088906714","https://openalex.org/W2107079154","https://openalex.org/W2121328026","https://openalex.org/W2295247391","https://openalex.org/W2622657084","https://openalex.org/W2730234337","https://openalex.org/W2953128905","https://openalex.org/W3106192328","https://openalex.org/W4254652536"],"related_works":["https://openalex.org/W623607250","https://openalex.org/W4245429118","https://openalex.org/W4245505501","https://openalex.org/W4255529442","https://openalex.org/W4212927854","https://openalex.org/W1545246811","https://openalex.org/W4236448199","https://openalex.org/W4383877548","https://openalex.org/W4232403550","https://openalex.org/W2136838521"],"abstract_inverted_index":{"A":[0,26],"factor":[1,76],"$$u$$":[2,22,31,48],"of":[3,10,21,36,44,47,58,71,91],"a":[4,8,37,41,55,68,75,88,119,136],"word":[5,27,42],"$$w$$":[6,11,16,24,28,84],"is":[7],"cover":[9,141],"if":[12],"every":[13],"position":[14],"in":[15,23,83,102],"lies":[17],"within":[18],"some":[19],"occurrence":[20],".":[25,49,85,123,147],"covered":[29],"by":[30],"thus":[32],"generalizes":[33],"the":[34],"idea":[35],"repetition,":[38],"that":[39,73,98],"is,":[40,74],"composed":[43],"exact":[45],"concatenations":[46],"In":[50],"this":[51],"article":[52],"we":[53,108],"introduce":[54],"new":[56],"notion":[57],"$$\\alpha":[59,80,114,121,138,144],"$$":[60,81,115,122,139],"-partial":[61,116,140],"cover,":[62,72],"which":[63,107],"can":[64,99],"be":[65,100],"viewed":[66],"as":[67],"relaxed":[69],"variant":[70],"covering":[77],"at":[78],"least":[79],"positions":[82],"We":[86,124],"develop":[87],"data":[89],"structure":[90],"$$\\mathcal":[92,103,130],"{O}(n)$$":[93],"size":[94],"(where":[95],"$$n=|w|$$":[96],")":[97],"constructed":[101],"{O}(n\\log":[104,131],"n)$$":[105,132],"time":[106],"apply":[109],"to":[110],"compute":[111],"all":[112],"shortest":[113,137],"covers":[117],"for":[118,128,142],"given":[120],"also":[125],"employ":[126],"it":[127],"an":[129],"-time":[133],"algorithm":[134],"computing":[135],"each":[143],"=1,2,\\ldots":[145],",n$$":[146]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
