{"id":"https://openalex.org/W3026254764","doi":"https://doi.org/10.1137/19m1249527","title":"Distributed $(\\Delta+1)$-Coloring via Ultrafast Graph Shattering","display_name":"Distributed $(\\Delta+1)$-Coloring via Ultrafast Graph Shattering","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3026254764","doi":"https://doi.org/10.1137/19m1249527","mag":"3026254764"},"language":"en","primary_location":{"id":"doi:10.1137/19m1249527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1249527","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061847213","display_name":"Yi\u2010Jun Chang","orcid":"https://orcid.org/0000-0002-0109-2432"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi-Jun Chang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101412259","display_name":"Wenzheng Li","orcid":"https://orcid.org/0009-0008-4536-8948"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenzheng Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076564426","display_name":"Seth Pettie","orcid":"https://orcid.org/0000-0002-0495-3904"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seth Pettie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6576,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87481884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"49","issue":"3","first_page":"497","last_page":"539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T12288","display_name":"Optimization and Search Problems","score":0.9991999864578247,"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/T10237","display_name":"Cryptography and Data Security","score":0.9970999956130981,"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/combinatorics","display_name":"Combinatorics","score":0.7660038471221924},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6266238689422607},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5661897659301758},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.534885823726654},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5170217752456665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49178555607795715},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44239863753318787},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.41539159417152405},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.33258599042892456},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32586488127708435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2803688645362854}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7660038471221924},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6266238689422607},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5661897659301758},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.534885823726654},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5170217752456665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49178555607795715},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44239863753318787},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.41539159417152405},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33258599042892456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32586488127708435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2803688645362854},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1249527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1249527","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6591826966","display_name":null,"funder_award_id":"CCF-1815316","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6809486582","display_name":null,"funder_award_id":"CCF-1637546","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8959633998","display_name":null,"funder_award_id":"CCF-1514383","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1957963525","https://openalex.org/W1964089073","https://openalex.org/W1970330908","https://openalex.org/W1997988698","https://openalex.org/W1998544343","https://openalex.org/W1998643836","https://openalex.org/W2009524061","https://openalex.org/W2048352893","https://openalex.org/W2048800330","https://openalex.org/W2053777090","https://openalex.org/W2054910423","https://openalex.org/W2056050680","https://openalex.org/W2056316084","https://openalex.org/W2065826935","https://openalex.org/W2100061495","https://openalex.org/W2136185479","https://openalex.org/W2467514673","https://openalex.org/W2797253418","https://openalex.org/W2907309485","https://openalex.org/W2913663107","https://openalex.org/W4233413206"],"related_works":["https://openalex.org/W3127082728","https://openalex.org/W2067936666","https://openalex.org/W2279830512","https://openalex.org/W3097369619","https://openalex.org/W2007715402","https://openalex.org/W3046990805","https://openalex.org/W4287691960","https://openalex.org/W2963181990","https://openalex.org/W2913663107","https://openalex.org/W2004524662"],"abstract_inverted_index":{"Vertex":[0],"coloring":[1,24,47,187,193,209],"is":[2,41,95,98,157,181,263],"one":[3],"of":[4,45,59,69,107,113,121,132,140,167,185,221,230,235,244],"the":[5,26,42,102,114,133,162,182,201,236],"classic":[6],"symmetry":[7],"breaking":[8],"problems":[9],"studied":[10],"in":[11,25,31],"distributed":[12,192],"computing.":[13],"In":[14],"this":[15,52],"paper,":[16],"we":[17],"present":[18],"a":[19,57,65,218],"new":[20],"algorithm":[21,68,106,229],"for":[22,198,205],"$(\\Delta+1)$-list":[23,186,208],"randomized":[27,67],"${LOCAL}$":[28],"model":[29],"running":[30,155],"$O({Det}_{\\scriptscriptstyle":[32],"d}(\\operatorname{poly}":[33],"\\log":[34],"n))=O(\\operatorname{poly}(\\log\\log":[35],"n))$":[36,164],"time,":[37],"where":[38,179],"${Det}_{\\scriptscriptstyle":[39,250],"d}(n')$":[40,251],"deterministic":[43,105,183,203,226],"complexity":[44,80,146,184],"$(\\deg+1)$-list":[46],"on":[48,119,138,188,212,242],"$n'$-vertex":[49,189],"graphs.":[50,190],"(In":[51],"problem,":[53],"each":[54],"$v$":[55],"has":[56,194],"palette":[58],"size":[60],"$\\deg(v)+1$.)":[61],"This":[62],"improves":[63],"upon":[64],"previous":[66],"Harris,":[70],"Schneider,":[71],"and":[72,110,126,129,170,207,232,252],"Su":[73],"[J.":[74],"ACM,":[75],"65":[76],"(2018),":[77],"19]":[78],"with":[79,145],"$O(\\sqrt{\\log":[81],"\\Delta}":[82],"+":[83,86,150],"\\log\\log":[84],"n":[85],"{Det}_{\\scriptscriptstyle":[87],"d}(\\operatorname{poly}\\log":[88],"n))":[89],"=":[90],"O(\\sqrt{\\log":[91],"n})$.":[92],"Unless":[93],"$\\Delta$":[94],"small,":[96],"it":[97],"also":[99],"faster":[100],"than":[101],"best":[103,202],"known":[104],"Fraigniaud,":[108],"Heinrich,":[109],"Kosowski":[111],"[Proceedings":[112,131,234],"57th":[115],"Annual":[116,135,238],"IEEE":[117],"Symposium":[118,137,241],"Foundations":[120],"Computer":[122],"Science":[123],"(FOCS),":[124],"2016]":[125],"Barenboim,":[127],"Elkin,":[128],"Goldenberg":[130],"38th":[134],"ACM":[136,239],"Principles":[139],"Distributed":[141],"Computing":[142,245],"(PODC),":[143],"2018],":[144],"$O(\\sqrt{\\Delta\\log":[147],"\\Delta}\\log^\\ast":[148],"\\Delta":[149],"\\log^*":[151],"n)$.":[152],"Our":[153],"algorithm's":[154],"time":[156],"syntactically":[158],"very":[159],"similar":[160],"to":[161],"$\\Omega({Det}(\\operatorname{poly}\\log":[163],"lower":[165],"bound":[166],"Chang,":[168],"Kopelowitz,":[169],"Pettie":[171],"[SIAM":[172],"J.":[173],"Comput.,":[174],"48":[175],"(2019),":[176],"pp.":[177],"122--143],":[178],"${Det}(n')$":[180,253],"Although":[191],"been":[195],"actively":[196],"investigated":[197],"30":[199],"years,":[200],"algorithms":[204],"$(\\deg+1)$-":[206],"(that":[210],"depend":[211],"$n'$":[213],"but":[214],"not":[215],"$\\Delta$)":[216],"use":[217],"black-box":[219],"application":[220],"network":[222,227],"decompositions.":[223],"The":[224],"recent":[225],"decomposition":[228],"Rozho\u0148":[231],"Ghaffari":[233],"52nd":[237],"SIGACT":[240],"Theory":[243],"(STOC),":[246],"2020]":[247],"implies":[248],"that":[249],"are":[254,260],"both":[255],"$\\operatorname{poly}(\\log":[256],"n')$.":[257],"Whether":[258],"they":[259],"asymptotically":[261],"equal":[262],"an":[264],"open":[265],"problem.":[266]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}