{"id":"https://openalex.org/W2963811310","doi":"https://doi.org/10.1137/16m1087667","title":"Deterministic Random Walks for Rapidly Mixing Chains","display_name":"Deterministic Random Walks for Rapidly Mixing Chains","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963811310","doi":"https://doi.org/10.1137/16m1087667","mag":"2963811310"},"language":"en","primary_location":{"id":"doi:10.1137/16m1087667","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1087667","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5067826040","display_name":"Takeharu Shiraga","orcid":"https://orcid.org/0000-0003-1236-9756"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takeharu Shiraga","raw_affiliation_strings":["Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103763741","display_name":"Yukiko Yamauchi","orcid":"https://orcid.org/0009-0009-8459-6676"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yukiko Yamauchi","raw_affiliation_strings":["Mathematical Informatics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Informatics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050611028","display_name":"Shuji Kijima","orcid":"https://orcid.org/0000-0001-6061-2330"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuji Kijima","raw_affiliation_strings":["Mathematical Informatics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Informatics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111575379","display_name":"Masafumi Yamashita","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masafumi Yamashita","raw_affiliation_strings":["Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6875,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74473253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"3","first_page":"2180","last_page":"2193"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9092000126838684,"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/markov-chain","display_name":"Markov chain","score":0.8409473299980164},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.7862034440040588},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7040396928787231},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.641021728515625},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.5983850955963135},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5296033620834351},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4976640045642853},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48825764656066895},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.480106383562088},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.4773856997489929},{"id":"https://openalex.org/keywords/markov-renewal-process","display_name":"Markov renewal process","score":0.4716842770576477},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.46350377798080444},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4564431309700012},{"id":"https://openalex.org/keywords/simple-random-sample","display_name":"Simple random sample","score":0.4354609549045563},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.42441806197166443},{"id":"https://openalex.org/keywords/examples-of-markov-chains","display_name":"Examples of Markov chains","score":0.4133000075817108},{"id":"https://openalex.org/keywords/irrational-number","display_name":"Irrational number","score":0.4108063578605652},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.3507145047187805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2205166518688202},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09648224711418152},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06490707397460938}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.8409473299980164},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.7862034440040588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7040396928787231},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.641021728515625},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.5983850955963135},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5296033620834351},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4976640045642853},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48825764656066895},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.480106383562088},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.4773856997489929},{"id":"https://openalex.org/C163540672","wikidata":"https://www.wikidata.org/wiki/Q1115431","display_name":"Markov renewal process","level":5,"score":0.4716842770576477},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46350377798080444},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4564431309700012},{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.4354609549045563},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.42441806197166443},{"id":"https://openalex.org/C76408418","wikidata":"https://www.wikidata.org/wiki/Q5419314","display_name":"Examples of Markov chains","level":5,"score":0.4133000075817108},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.4108063578605652},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3507145047187805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2205166518688202},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09648224711418152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06490707397460938},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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:10.1137/16m1087667","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1087667","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G125139516","display_name":"Theory for self-optimization of distributed systems","funder_award_id":"15K15938","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2362195281","display_name":"\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u8131\u4e71\u629e\u5316\uff1a\u6c7a\u5b9a\u6027\u8fd1\u4f3c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u306b\u5bfe\u3059\u308b\u65b0\u3057\u3044\u6c4e\u7528\u624b\u6cd5\u306e\u958b\u767a","funder_award_id":"15J03840","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3990214110","display_name":"Analysis of distributed load balancing algorithms on inhomogeneous and dynamic networks","funder_award_id":"17H07116","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5057265379","display_name":"Understanding the function and effect of randomness in probabilistic algorithms","funder_award_id":"25700002","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8479111029","display_name":"\u5206\u6563\u8a08\u7b97\u306b\u304a\u3051\u308b\u901a\u4fe1\u6a5f\u80fd\u306e\u5f79\u5272","funder_award_id":"15H02666","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1508237135","https://openalex.org/W1643282477","https://openalex.org/W1964285561","https://openalex.org/W1972007456","https://openalex.org/W1973374963","https://openalex.org/W1975911106","https://openalex.org/W1978196657","https://openalex.org/W1978598282","https://openalex.org/W1993292086","https://openalex.org/W2005107874","https://openalex.org/W2006397962","https://openalex.org/W2014474286","https://openalex.org/W2018777507","https://openalex.org/W2024766920","https://openalex.org/W2033900415","https://openalex.org/W2043805242","https://openalex.org/W2091309969","https://openalex.org/W2102663108","https://openalex.org/W2113295388","https://openalex.org/W2117204986","https://openalex.org/W2130608828","https://openalex.org/W2137795931","https://openalex.org/W2140262981","https://openalex.org/W2161611531","https://openalex.org/W2167628842","https://openalex.org/W2222348553","https://openalex.org/W2623400422","https://openalex.org/W2763355822","https://openalex.org/W2962850529","https://openalex.org/W2963111489","https://openalex.org/W3106228637","https://openalex.org/W4231961887"],"related_works":["https://openalex.org/W2393764248","https://openalex.org/W3023188449","https://openalex.org/W2141396792","https://openalex.org/W292716529","https://openalex.org/W4235599811","https://openalex.org/W4250947215","https://openalex.org/W1565315865","https://openalex.org/W4244907444","https://openalex.org/W4381104073","https://openalex.org/W2328055495"],"abstract_inverted_index":{"The":[0],"rotor-router":[1,24],"model":[2,25,51,80],"is":[3],"a":[4,9,14,49,54],"deterministic":[5],"process":[6],"analogous":[7],"to":[8],"simple":[10,43],"random":[11,29,44],"walk":[12,30],"on":[13],"graph,":[15],"and":[16,26,81,86],"the":[17,23,69,73,78,92,97,101],"discrepancy":[18,71,93],"of":[19,72,75,91,96,100],"token":[20],"configurations":[21],"between":[22,77],"its":[27,82],"corresponding":[28,83],"has":[31],"been":[32],"investigated":[33],"in":[34,94],"some":[35],"contexts.":[36],"Motivated":[37],"by":[38],"general":[39],"Markov":[40,55,84,102],"chains":[41],"beyond":[42],"walks,":[45],"this":[46],"paper":[47],"investigates":[48],"generalized":[50,79],"which":[52],"imitates":[53],"chain":[56],"(of":[57],"multiple":[58],"tokens)":[59],"possibly":[60],"containing":[61],"irrational":[62],"transition":[63],"probabilities.":[64],"We":[65],"are":[66],"concerned":[67],"with":[68],"vertexwise":[70],"numbers":[74],"tokens":[76],"chain,":[85],"present":[87],"an":[88],"upper":[89],"bound":[90],"terms":[95],"mixing":[98],"time":[99],"chain.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
