{"id":"https://openalex.org/W1601888115","doi":"https://doi.org/10.1007/s00453-014-9931-3","title":"One-Variable Word Equations in Linear Time","display_name":"One-Variable Word Equations in Linear Time","publication_year":2014,"publication_date":"2014-09-10","ids":{"openalex":"https://openalex.org/W1601888115","doi":"https://doi.org/10.1007/s00453-014-9931-3","mag":"1601888115"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-014-9931-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9931-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9931-3.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/s00453-014-9931-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066525178","display_name":"Artur Je\u017c","orcid":"https://orcid.org/0000-0003-4321-3105"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"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"]}],"countries":["DE","PL"],"is_corresponding":true,"raw_author_name":"Artur Je\u017c","raw_affiliation_strings":["Institute of Computer Science, University of Wroc\u0142aw, ul.\u00a0Joliot-Curie 15, 50-383\u00a0, Wroc\u0142aw, Poland","Max Planck Institute f\u00fc Informatik, 66123 Campus E1 4, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Wroc\u0142aw, ul.\u00a0Joliot-Curie 15, 50-383\u00a0, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]},{"raw_affiliation_string":"Max Planck Institute f\u00fc Informatik, 66123 Campus E1 4, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066525178"],"corresponding_institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210109712"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":3.6811,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.93351756,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"74","issue":"1","first_page":"1","last_page":"48"},"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":0.9994000196456909,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.7785993218421936},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.7330716848373413},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.7197967767715454},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6454776525497437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5649446249008179},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.5493289828300476},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4736522436141968},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42945414781570435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3833597004413605},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.352250337600708},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3425760567188263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32403796911239624},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21648985147476196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14330217242240906},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08420473337173462}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7785993218421936},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.7330716848373413},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.7197967767715454},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6454776525497437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5649446249008179},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.5493289828300476},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4736522436141968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42945414781570435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3833597004413605},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.352250337600708},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3425760567188263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32403796911239624},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21648985147476196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14330217242240906},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08420473337173462}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-014-9931-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9931-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9931-3.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"}],"best_oa_location":{"id":"doi:10.1007/s00453-014-9931-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-014-9931-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-014-9931-3.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/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1601888115.pdf","grobid_xml":"https://content.openalex.org/works/W1601888115.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W134255016","https://openalex.org/W1489909987","https://openalex.org/W1492050056","https://openalex.org/W1506622179","https://openalex.org/W1546860696","https://openalex.org/W1730038947","https://openalex.org/W1755286175","https://openalex.org/W1989660382","https://openalex.org/W1993370765","https://openalex.org/W2006565583","https://openalex.org/W2028685566","https://openalex.org/W2037286444","https://openalex.org/W2041189577","https://openalex.org/W2067974452","https://openalex.org/W2092901467","https://openalex.org/W2132809979","https://openalex.org/W2171035269","https://openalex.org/W2189745519","https://openalex.org/W2275139177","https://openalex.org/W2344943271","https://openalex.org/W2624305728","https://openalex.org/W2761224894","https://openalex.org/W2953070628","https://openalex.org/W3138321435"],"related_works":["https://openalex.org/W2059442203","https://openalex.org/W2595899102","https://openalex.org/W2421475109","https://openalex.org/W4297792110","https://openalex.org/W1629505938","https://openalex.org/W2963209704","https://openalex.org/W1504650505","https://openalex.org/W1676587966","https://openalex.org/W1483438220","https://openalex.org/W2415632638"],"abstract_inverted_index":{"In":[0],"this":[1,34],"paper":[2],"we":[3],"consider":[4],"word":[5,25],"equations":[6],"with":[7],"one-variable":[8,47],"(and":[9],"arbitrarily":[10],"many":[11],"occurrences":[12,69],"of":[13,18,46,68,70,91,116],"it).":[14],"A":[15],"recent":[16],"technique":[17],"recompression,":[19],"which":[20],"is":[21,27,42,55,65,103],"applicable":[22],"to":[23,29,83,105],"general":[24,38],"equations,":[26],"shown":[28],"be":[30],"suitable":[31],"also":[32],"in":[33,37,44,73,108],"case.":[35],"While":[36],"case":[39,45],"the":[40,66,71,74,78,100,109],"recompression":[41],"nondeterministic":[43],"it":[48],"becomes":[49],"deterministic":[50],"and":[51,85],"its":[52],"running":[53,101],"time":[54,98,102],"$$\\mathcal":[56,106],"{O}(n":[57],"+":[58],"\\#_X":[59],"\\log":[60],"n)$$":[61],",":[62],"where":[63],"$$\\#_X$$":[64],"number":[67],"variable":[72],"equation.":[75],"This":[76],"matches":[77],"previously":[79],"best":[80],"algorithm":[81],"due":[82],"D\u0105browski":[84],"Plandowski.":[86],"Then,":[87],"using":[88],"a":[89],"couple":[90],"heuristics":[92],"as":[93,95],"well":[94],"more":[96],"detailed":[97],"analysis,":[99],"lowered":[104],"{O}(n)$$":[107],"RAM":[110],"model.":[111],"Unfortunately,":[112],"no":[113],"new":[114],"properties":[115],"solutions":[117],"are":[118],"shown.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
