{"id":"https://openalex.org/W7131104686","doi":"https://doi.org/10.48550/arxiv.2602.18188","title":"It does not matter how you define locally checkable labelings","display_name":"It does not matter how you define locally checkable labelings","publication_year":2026,"publication_date":"2026-02-20","ids":{"openalex":"https://openalex.org/W7131104686","doi":"https://doi.org/10.48550/arxiv.2602.18188"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.18188","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078408424","display_name":"Antonio Cruciani","orcid":"https://orcid.org/0000-0002-9538-4275"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cruciani, Antonio","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025342406","display_name":"Avinandan Das","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Das, Avinandan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120092317","display_name":"Alesya Raevskaya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raevskaya, Alesya","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126141338","display_name":"Jukka Suomela","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suomela, Jukka","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078408424"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5913000106811523,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5913000106811523,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.2224999964237213,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.05119999870657921,"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/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.6442000269889832},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5478000044822693},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.35690000653266907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.32280001044273376},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3147999942302704},{"id":"https://openalex.org/keywords/graph-rewriting","display_name":"Graph rewriting","score":0.30660000443458557}],"concepts":[{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.6442000269889832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5680999755859375},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5478000044822693},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4596000015735626},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3370000123977661},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31869998574256897},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C558772884","wikidata":"https://www.wikidata.org/wiki/Q1508564","display_name":"Graph rewriting","level":3,"score":0.30660000443458557},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.18188","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.18188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18188","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.18188","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"score":0.43194350600242615,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Locally":[0],"checkable":[1,138],"labeling":[2],"problems":[3,31,61,71,108,124,139,157],"(LCLs)":[4],"form":[5],"the":[6,9,19,102,120,141,163,175,195,206],"foundation":[7],"of":[8,12,41,60,74,106,122,136,165],"modern":[10],"theory":[11],"distributed":[13,103],"graph":[14,30],"algorithms.":[15],"First":[16],"introduced":[17],"in":[18,79,182,205],"seminal":[20],"paper":[21],"by":[22,36],"Naor":[23],"and":[24,193],"Stockmeyer":[25],"[STOC":[26],"1993],":[27],"these":[28],"are":[29,57,73,179],"that":[32,62,67,72,86,94,119,170,185],"can":[33,172],"be":[34],"described":[35],"listing":[37],"a":[38,50,58,132,190],"finite":[39],"set":[40],"valid":[42],"local":[43,180],"neighborhoods.":[44],"This":[45],"seemingly":[46],"simple":[47],"definition":[48],"strikes":[49],"careful":[51],"balance":[52],"between":[53,174],"two":[54,176],"objectives:":[55],"they":[56],"family":[59,121,135],"is":[63,88,109,125,197],"broad":[64],"enough":[65,84],"so":[66,85],"it":[68,87],"captures":[69],"numerous":[70],"interest":[75],"to":[76,90,128,150,161,189],"researchers":[77],"working":[78],"this":[80,115],"field,":[81],"yet":[82],"restrictive":[83],"possible":[89],"prove":[91],"strong":[92],"theorems":[93],"hold":[95],"for":[96],"all":[97],"LCL":[98,107,123],"problems.":[99],"In":[100,114],"particular,":[101],"complexity":[104],"landscape":[105],"now":[110],"very":[111,133],"well":[112],"understood.":[113],"work":[116],"we":[117],"show":[118,169],"extremely":[126],"robust":[127],"variations.":[129],"We":[130,168],"present":[131],"restricted":[134,149],"locally":[137],"(essentially,":[140],"\"node-edge":[142],"checkable\"":[143],"formalism":[144],"familiar":[145],"from":[146],"round":[147],"elimination,":[148],"regular":[151],"unlabeled":[152],"graphs);":[153],"most":[154,199],"importantly,":[155],"such":[156],"cannot":[158],"directly":[159],"refer":[160],"e.g.":[162],"existence":[164],"short":[166],"cycles.":[167],"one":[171],"translate":[173],"formalisms":[177],"(there":[178],"reductions":[181],"both":[183],"directions":[184],"only":[186],"need":[187],"access":[188],"symmetry-breaking":[191],"oracle,":[192],"hence":[194],"overhead":[196],"at":[198],"an":[200],"additive":[201],"$O(\\log^*":[202],"n)$":[203],"rounds":[204],"LOCAL":[207],"model).":[208]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-24T00:00:00"}
