{"id":"https://openalex.org/W2610464835","doi":"https://doi.org/10.1145/3278158","title":"A Universal Tree Balancing Theorem","display_name":"A Universal Tree Balancing Theorem","publication_year":2018,"publication_date":"2018-10-22","ids":{"openalex":"https://openalex.org/W2610464835","doi":"https://doi.org/10.1145/3278158","mag":"2610464835"},"language":"en","primary_location":{"id":"doi:10.1145/3278158","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3278158","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1704.08705","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005654849","display_name":"Moses Ganardi","orcid":"https://orcid.org/0000-0002-0775-7781"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Moses Ganardi","raw_affiliation_strings":["University of Siegen, Germany","(University of Siegen), Germany"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"(University of Siegen), Germany","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Lohrey","raw_affiliation_strings":["University of Siegen, Germany","(University of Siegen), Germany"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"(University of Siegen), Germany","institution_ids":["https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005654849"],"corresponding_institution_ids":["https://openalex.org/I206895457"],"apc_list":null,"apc_paid":null,"fwci":0.2133,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51133966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"1","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9990000128746033,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987999796867371,"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/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/semiring","display_name":"Semiring","score":0.7855191230773926},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7068076133728027},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6820457577705383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6265121102333069},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6075196862220764},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5666446089744568},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5292474627494812},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46139857172966003},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4074397683143616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32888656854629517},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11337879300117493},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10927808284759521},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10714229941368103}],"concepts":[{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.7855191230773926},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7068076133728027},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6820457577705383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6265121102333069},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6075196862220764},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5666446089744568},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5292474627494812},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46139857172966003},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4074397683143616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32888656854629517},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11337879300117493},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10927808284759521},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10714229941368103},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3278158","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3278158","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1704.08705","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.08705","pdf_url":"https://arxiv.org/pdf/1704.08705","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2610464835","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1704.08705.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.1704.08705","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1704.08705","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1704.08705","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.08705","pdf_url":"https://arxiv.org/pdf/1704.08705","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2610464835.pdf","grobid_xml":"https://content.openalex.org/works/W2610464835.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W41330591","https://openalex.org/W115737229","https://openalex.org/W1595778895","https://openalex.org/W1754942486","https://openalex.org/W1965874601","https://openalex.org/W1990870868","https://openalex.org/W1992524974","https://openalex.org/W2009269558","https://openalex.org/W2024091095","https://openalex.org/W2027501230","https://openalex.org/W2038247515","https://openalex.org/W2038793519","https://openalex.org/W2041211107","https://openalex.org/W2045583484","https://openalex.org/W2068638452","https://openalex.org/W2069796292","https://openalex.org/W2081256023","https://openalex.org/W2085012646","https://openalex.org/W2113004376","https://openalex.org/W2119630998","https://openalex.org/W2123297015","https://openalex.org/W2130566259","https://openalex.org/W2138170131","https://openalex.org/W2170478756","https://openalex.org/W2174735959","https://openalex.org/W2889360129","https://openalex.org/W2962878694","https://openalex.org/W2963295241","https://openalex.org/W2963905622","https://openalex.org/W4388289494"],"related_works":["https://openalex.org/W2514492620","https://openalex.org/W2990947232","https://openalex.org/W1982818703","https://openalex.org/W2776057122","https://openalex.org/W2951424111","https://openalex.org/W1675346939","https://openalex.org/W2113350754","https://openalex.org/W3102609340","https://openalex.org/W276335716","https://openalex.org/W2352767712","https://openalex.org/W1816810082","https://openalex.org/W3046947725","https://openalex.org/W2168359059","https://openalex.org/W2767521804","https://openalex.org/W2255083403","https://openalex.org/W2078845413","https://openalex.org/W2963698582","https://openalex.org/W2104715607","https://openalex.org/W2774239358","https://openalex.org/W2963192233"],"abstract_inverted_index":{"We":[0],"present":[1,84],"a":[2,34,55,63,118,135,186],"general":[3],"framework":[4],"for":[5,54,134,156,189],"balancing":[6],"expressions":[7,155,191],"(terms)":[8],"in":[9,61,95,165],"the":[10,25,37,83,90,103,113,144],"form":[11],"of":[12,58,67,172],"so-called":[13],"tree":[14,64],"straight-line":[15,65],"programs.":[16],"The":[17],"latter":[18],"can":[19,52,92,162],"be":[20,93,163],"seen":[21],"as":[22],"circuits":[23,171],"over":[24,107,117],"free":[26],"term":[27,57,104,114],"algebra":[28,110,121],"extended":[29],"by":[30,138],"contexts":[31],"(terms":[32],"with":[33],"hole)":[35],"and":[36,73,175],"operations,":[38],"which":[39],"insert":[40],"terms/contexts":[41],"into":[42,169],"contexts.":[43],"In":[44,82],"Ref.":[45],"[16],":[46],"it":[47,86,151],"was":[48],"shown":[49,88,153],"that":[50,89,154],"one":[51],"compute":[53],"given":[56],"size":[59,74,176],"n":[60,71,77,80,179,182],"logspace":[62],"program":[66],"depth":[68,174],"O":[69,75,177],"(log":[70],")":[72],"(":[76,123,178],"/":[78,180],"log":[79,181],").":[81,125],"article,":[85],"is":[87,148,152,192],"conversion":[91],"done":[94],"DLOGTIME-uniform":[96,166],"TC":[97,167],"0":[98,168],".":[99],"This":[100],"allows":[101],"reducing":[102],"evaluation":[105,115,146],"problem":[106,116,147],"an":[108,131,157],"arbitrary":[109,158],"A":[111,124],"to":[112],"derived":[119],"two-sorted":[120],"F":[122],"Three":[126],"applications":[127],"are":[128],"presented:":[129],"(i)":[130],"alternative":[132],"proof":[133],"recent":[136],"result":[137,188],"Krebs":[139],"et":[140],"al.":[141],"[25]":[142],"on":[143],"expression":[145],"given;":[149],"(ii)":[150],"(possibly":[159],"non-commutative)":[160],"semiring":[161],"transformed":[164],"equivalent":[170],"logarithmic":[173],");":[183],"and,":[184],"(iii)":[185],"corresponding":[187],"regular":[190],"shown.":[193]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
