{"id":"https://openalex.org/W2944363028","doi":"https://doi.org/10.1109/lics.2019.8785694","title":"Walk refinement, walk logic, and the iteration number of the Weisfeiler-Leman algorithm","display_name":"Walk refinement, walk logic, and the iteration number of the Weisfeiler-Leman algorithm","publication_year":2019,"publication_date":"2019-06-01","ids":{"openalex":"https://openalex.org/W2944363028","doi":"https://doi.org/10.1109/lics.2019.8785694","mag":"2944363028"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2019.8785694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.03008","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050723678","display_name":"Moritz Lichter","orcid":"https://orcid.org/0000-0001-5437-8074"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I4387152675","display_name":"Rheinland-Pf\u00e4lzische Technische Universit\u00e4t Kaiserslautern-Landau","ror":"https://ror.org/01qrts582","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387152675"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz Lichter","raw_affiliation_strings":["TU Kaiserslautern","University of Kaiserslautern"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Kaiserslautern","institution_ids":["https://openalex.org/I153267046","https://openalex.org/I4387152675"]},{"raw_affiliation_string":"University of Kaiserslautern","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036540193","display_name":"Ilia Ponomarenko","orcid":"https://orcid.org/0000-0003-2444-731X"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ilia Ponomarenko","raw_affiliation_strings":["St. Petersburg Department of Steklov, Mathematical Institute of the Russian Academy of Sciences","Russian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"St. Petersburg Department of Steklov, Mathematical Institute of the Russian Academy of Sciences","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I1313323035"]},{"raw_affiliation_string":"Russian Academy of Sciences","institution_ids":["https://openalex.org/I1313323035"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017685495","display_name":"Pascal Schweitzer","orcid":"https://orcid.org/0009-0001-3585-8213"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I4387152675","display_name":"Rheinland-Pf\u00e4lzische Technische Universit\u00e4t Kaiserslautern-Landau","ror":"https://ror.org/01qrts582","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387152675"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pascal Schweitzer","raw_affiliation_strings":["TU Kaiserslautern","University of Kaiserslautern"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Kaiserslautern","institution_ids":["https://openalex.org/I153267046","https://openalex.org/I4387152675"]},{"raw_affiliation_string":"University of Kaiserslautern","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1926,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51481423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9983000159263611,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.691655158996582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6415306925773621},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5665984749794006},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.47796058654785156},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.45784372091293335},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.427114337682724},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.42022988200187683},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3611726760864258}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.691655158996582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6415306925773621},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5665984749794006},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.47796058654785156},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.45784372091293335},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.427114337682724},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.42022988200187683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3611726760864258},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/lics.2019.8785694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2019.8785694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1905.03008","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.03008","pdf_url":"https://arxiv.org/pdf/1905.03008","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":null,"raw_type":"text"},{"id":"mag:2944363028","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.03008","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.1905.03008","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.03008","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.03008","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.03008","pdf_url":"https://arxiv.org/pdf/1905.03008","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":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6000000238418579,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944363028.pdf","grobid_xml":"https://content.openalex.org/works/W2944363028.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W168459216","https://openalex.org/W565809675","https://openalex.org/W1485862647","https://openalex.org/W1517098132","https://openalex.org/W1522668611","https://openalex.org/W2152035036","https://openalex.org/W2181072414","https://openalex.org/W2409645877","https://openalex.org/W2743930031","https://openalex.org/W2963494352","https://openalex.org/W2963584216","https://openalex.org/W2964195552","https://openalex.org/W4213243275","https://openalex.org/W4246560108","https://openalex.org/W6726212349"],"related_works":["https://openalex.org/W2966519690","https://openalex.org/W2964195552","https://openalex.org/W3126958641","https://openalex.org/W2952965188","https://openalex.org/W2911738047","https://openalex.org/W2083951446","https://openalex.org/W2149131635","https://openalex.org/W2055656009","https://openalex.org/W2525537616","https://openalex.org/W2963978854","https://openalex.org/W2341570704","https://openalex.org/W2621997583","https://openalex.org/W2970774353","https://openalex.org/W1590467876","https://openalex.org/W2182026046","https://openalex.org/W2071824433","https://openalex.org/W2100239335","https://openalex.org/W2952763318","https://openalex.org/W1617257399","https://openalex.org/W3109156225"],"abstract_inverted_index":{"We":[0,81,113],"show":[1],"that":[2,19,65,125],"the":[3,71,91,96,129],"2-dimensional":[4],"Weisfeiler-Leman":[5,73],"algorithm":[6],"stabilizes":[7],"n-vertex":[8],"graphs":[9,22],"after":[10],"at":[11,47,76],"most":[12,48,77],"O(n":[13,49],"log":[14,50],"n)":[15],"iterations.":[16],"This":[17,99],"implies":[18],"if":[20],"such":[21],"are":[23],"distinguishable":[24],"in":[25,38],"3-variable":[26],"first":[27],"order":[28],"logic":[29,40,118],"with":[30,102],"counting,":[31],"then":[32,82],"they":[33],"can":[34],"also":[35,114],"be":[36],"distinguished":[37],"this":[39,53],"by":[41,75,106],"a":[42,56,78,116,120],"formula":[43],"of":[44,93,95,109],"quantifier":[45],"depth":[46],"n).":[51],"For":[52],"we":[54],"exploit":[55],"new":[57,130],"refinement":[58,74],"based":[59],"on":[60,90],"counting":[61],"walks":[62],"and":[63,87,119],"argue":[64],"its":[66],"iteration":[67],"number":[68,92],"differs":[69],"from":[70],"classic":[72],"logarithmic":[79],"factor.":[80],"prove":[83],"matching":[84],"linear":[85],"upper":[86],"lower":[88],"bounds":[89],"iterations":[94],"walk":[97,117,122,131],"refinement.":[98,132],"is":[100],"achieved":[101],"an":[103],"algebraic":[104],"approach":[105],"exploiting":[107],"properties":[108],"semisimple":[110],"matrix":[111],"algebras.":[112],"define":[115],"bijective":[121],"pebble":[123],"game":[124],"precisely":[126],"correspond":[127],"to":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}