{"id":"https://openalex.org/W2998696354","doi":"https://doi.org/10.1145/3357713.3384244","title":"Improved bounds for perfect sampling of k-colorings in graphs","display_name":"Improved bounds for perfect sampling of k-colorings in graphs","publication_year":2020,"publication_date":"2020-06-07","ids":{"openalex":"https://openalex.org/W2998696354","doi":"https://doi.org/10.1145/3357713.3384244","mag":"2998696354"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384244","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384244","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.10323","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052705780","display_name":"Siddharth Bhandari","orcid":"https://orcid.org/0000-0003-3481-6078"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Siddharth Bhandari","raw_affiliation_strings":["Tata Institute of Fundamental Research, India","Tata Institute of Fundamental Research, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, India","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"Tata Institute of Fundamental Research, India#TAB#","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101727280","display_name":"Sayantan Chakraborty","orcid":"https://orcid.org/0000-0002-7246-0589"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sayantan Chakraborty","raw_affiliation_strings":["Tata Institute of Fundamental Research, India","Tata Institute of Fundamental Research, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, India","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"Tata Institute of Fundamental Research, India#TAB#","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11947397"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00956417,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":null,"first_page":"631","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965000152587891,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9480999708175659,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/combinatorics","display_name":"Combinatorics","score":0.8240549564361572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7426574230194092},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5905776619911194},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.5277717113494873},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5029131770133972},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5018835067749023},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4573054611682892},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4508400559425354},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45076167583465576},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4153464436531067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12636816501617432}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8240549564361572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7426574230194092},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5905776619911194},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.5277717113494873},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5029131770133972},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5018835067749023},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4573054611682892},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4508400559425354},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45076167583465576},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4153464436531067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12636816501617432},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3357713.3384244","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384244","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1909.10323","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10323","pdf_url":"https://arxiv.org/pdf/1909.10323","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"doi:10.48550/arxiv.1909.10323","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.10323","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},{"id":"mag:2998696354","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc26.html#BhandariC19","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.10323","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10323","pdf_url":"https://arxiv.org/pdf/1909.10323","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2998696354.pdf","grobid_xml":"https://content.openalex.org/works/W2998696354.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W9125994","https://openalex.org/W1976445742","https://openalex.org/W1977321916","https://openalex.org/W2011373957","https://openalex.org/W2012032973","https://openalex.org/W2033900415","https://openalex.org/W2072696811","https://openalex.org/W2109260999","https://openalex.org/W2140422174","https://openalex.org/W2898624802","https://openalex.org/W2914272038","https://openalex.org/W3111890340"],"related_works":["https://openalex.org/W3034989894","https://openalex.org/W3173624684","https://openalex.org/W2185076815","https://openalex.org/W2104639020","https://openalex.org/W2965200911","https://openalex.org/W3183157744","https://openalex.org/W2069816168","https://openalex.org/W1691921959","https://openalex.org/W2903540361","https://openalex.org/W3128980175","https://openalex.org/W3168179120","https://openalex.org/W2950692115","https://openalex.org/W1601593591","https://openalex.org/W2949907752","https://openalex.org/W1565384686","https://openalex.org/W2145192475","https://openalex.org/W2951254008","https://openalex.org/W1797876130","https://openalex.org/W2022490362","https://openalex.org/W3037316276"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,26,60,68],"randomized":[3],"algorithm":[4,53,73,81],"that":[5],"takes":[6],"as":[7],"input":[8],"an":[9,19],"undirected":[10],"n-vertex":[11],"graph":[12],"G":[13],"with":[14,82,93],"maximum":[15],"degree":[16],"\u0394":[17],"and":[18,24],"integer":[20],"k":[21],">":[22],"3\u0394,":[23],"returns":[25],"random":[27],"proper":[28,45],"k-coloring":[29],"of":[30,34,43,51,62,96],"G.":[31],"The":[32],"distribution":[33],"the":[35,41,47,52],"coloring":[36],"is":[37,54],"perfectly":[38,91],"uniform":[39],"over":[40],"set":[42],"all":[44],"k-colorings;":[46],"expected":[48,83],"running":[49,84],"time":[50,70,85],"poly(k,n)=O(n\u03942\u00b7":[55],"log(k)).":[56],"This":[57],"improves":[58],"upon":[59],"result":[61],"Huber":[63],"(STOC":[64],"1998)":[65],"who":[66],"obtained":[67],"polynomial":[69],"perfect":[71],"sampling":[72,92],"for":[74],"k>\u03942+2\u0394.":[75],"Prior":[76],"to":[77,89],"our":[78],"work,":[79],"no":[80],"poly(k,n)":[86],"was":[87],"known":[88],"guarantee":[90],"sub-quadratic":[94],"number":[95],"colors":[97],"in":[98],"general.":[99]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}