{"id":"https://openalex.org/W2752046352","doi":"https://doi.org/10.1109/tac.2019.2895299","title":"On the Structure and Computation of Random Walk Times in Finite Graphs","display_name":"On the Structure and Computation of Random Walk Times in Finite Graphs","publication_year":2019,"publication_date":"2019-01-25","ids":{"openalex":"https://openalex.org/W2752046352","doi":"https://doi.org/10.1109/tac.2019.2895299","mag":"2752046352"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2895299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2895299","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.01633","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004774385","display_name":"Andrew Clark","orcid":"https://orcid.org/0000-0002-5868-6186"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Clark","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, USA","Department of Electrical & Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA"],"raw_orcid":"https://orcid.org/0000-0002-5868-6186","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, USA","institution_ids":["https://openalex.org/I107077323"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019524943","display_name":"Basel Alomair","orcid":"https://orcid.org/0000-0002-0494-2586"},"institutions":[{"id":"https://openalex.org/I1284598098","display_name":"King Abdulaziz City for Science and Technology","ror":"https://ror.org/05tdz6m39","country_code":"SA","type":"facility","lineage":["https://openalex.org/I1284598098"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Basel Alomair","raw_affiliation_strings":["Center for Cybersecurity, King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia","Center for Cybersecurity, King Abdulaziz City for Sci. & Technol., Riyadh, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0494-2586","affiliations":[{"raw_affiliation_string":"Center for Cybersecurity, King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I1284598098"]},{"raw_affiliation_string":"Center for Cybersecurity, King Abdulaziz City for Sci. & Technol., Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I1284598098"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003489427","display_name":"Linda Bushnell","orcid":"https://orcid.org/0000-0002-8751-2409"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linda Bushnell","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Washington, Seattle, USA","[Department of Electrical, and Computer Engineering, University of Washington, Seattle, WA, USA]"],"raw_orcid":"https://orcid.org/0000-0002-8751-2409","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Washington, Seattle, USA","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I58610484"]},{"raw_affiliation_string":"[Department of Electrical, and Computer Engineering, University of Washington, Seattle, WA, USA]","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079723268","display_name":"Radha Poovendran","orcid":"https://orcid.org/0000-0003-0269-8097"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Radha Poovendran","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Washington, Seattle, USA","[Department of Electrical, and Computer Engineering, University of Washington, Seattle, WA, USA]"],"raw_orcid":"https://orcid.org/0000-0003-0269-8097","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Washington, Seattle, USA","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I58610484"]},{"raw_affiliation_string":"[Department of Electrical, and Computer Engineering, University of Washington, Seattle, WA, USA]","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00821766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"64","issue":"11","first_page":"4470","last_page":"4483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9986000061035156,"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":0.9962999820709229,"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/random-walk","display_name":"Random walk","score":0.8611732125282288},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.602033257484436},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5836402773857117},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5699729919433594},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5422578454017639},{"id":"https://openalex.org/keywords/hitting-time","display_name":"Hitting time","score":0.4804365336894989},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.46578139066696167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46002689003944397},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4439631700515747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44306546449661255},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.42868366837501526},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42317330837249756},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3174128532409668},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3057177662849426},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07718950510025024}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.8611732125282288},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.602033257484436},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5836402773857117},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5699729919433594},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5422578454017639},{"id":"https://openalex.org/C199277547","wikidata":"https://www.wikidata.org/wiki/Q5872687","display_name":"Hitting time","level":2,"score":0.4804365336894989},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.46578139066696167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46002689003944397},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4439631700515747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44306546449661255},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.42868366837501526},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42317330837249756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3174128532409668},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3057177662849426},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07718950510025024},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2019.2895299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2895299","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.01633","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.01633","pdf_url":"https://arxiv.org/pdf/1709.01633","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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1709.01633","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1709.01633","pdf_url":"https://arxiv.org/pdf/1709.01633","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:2752046352","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1709.01633","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.1709.01633","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.01633","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:oai:arXiv.org:1709.01633","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.01633","pdf_url":"https://arxiv.org/pdf/1709.01633","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":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1637523201","display_name":null,"funder_award_id":"N00014-17-1-2946","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G1956726121","display_name":"CPS: TTP Option: Synergy: Collaborative Research: Certifiable, Scalable, and Attack-resilient Submodular Control Framework for Smart Grid Stability","funder_award_id":"1544173","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4504108201","display_name":null,"funder_award_id":"N00014-17-1","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7075259197","display_name":null,"funder_award_id":"CNS-1544173","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8325026323","display_name":null,"funder_award_id":"N00014-16-1-2710","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8906680872","display_name":null,"funder_award_id":"N00014-16-1-2710","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"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1498432697","https://openalex.org/W1586184796","https://openalex.org/W1600293573","https://openalex.org/W1653616422","https://openalex.org/W1703742514","https://openalex.org/W1943821960","https://openalex.org/W1964535518","https://openalex.org/W1968695868","https://openalex.org/W1968817778","https://openalex.org/W2019854450","https://openalex.org/W2029828838","https://openalex.org/W2032100464","https://openalex.org/W2048572907","https://openalex.org/W2059470663","https://openalex.org/W2098432798","https://openalex.org/W2117905067","https://openalex.org/W2118958806","https://openalex.org/W2129579944","https://openalex.org/W2130470622","https://openalex.org/W2136647665","https://openalex.org/W2159000620","https://openalex.org/W2160588912","https://openalex.org/W2161984370","https://openalex.org/W2165744313","https://openalex.org/W2167064216","https://openalex.org/W2170807097","https://openalex.org/W2235884325","https://openalex.org/W2512154443","https://openalex.org/W2568545994","https://openalex.org/W2633443989","https://openalex.org/W2963300745","https://openalex.org/W3105471108","https://openalex.org/W4205533198","https://openalex.org/W4230376356","https://openalex.org/W6634934147","https://openalex.org/W6966415830"],"related_works":["https://openalex.org/W2051527191","https://openalex.org/W3171278913","https://openalex.org/W2898697591","https://openalex.org/W2064087447","https://openalex.org/W2964484857","https://openalex.org/W3096216834","https://openalex.org/W2160504298","https://openalex.org/W3098556930","https://openalex.org/W1847535063","https://openalex.org/W2791678910","https://openalex.org/W2263088437","https://openalex.org/W3003363271","https://openalex.org/W3172951351","https://openalex.org/W1907296788","https://openalex.org/W1643282477","https://openalex.org/W2760154051","https://openalex.org/W3083123380","https://openalex.org/W2918498316","https://openalex.org/W2494102703","https://openalex.org/W2605290762"],"abstract_inverted_index":{"We":[0,100,120],"consider":[1],"random":[2,70,98],"walks":[3],"in":[4,9,24,42,53,96,128],"which":[5,129],"the":[6,32,36,44,65,69,77,85,130,141],"walk":[7,33,71],"originates":[8],"one":[10,20],"set":[11,38,78],"of":[12,40,46,68,76,79,105,111,117],"nodes":[13,23],"and":[14,57,82,88,133],"then":[15],"continues":[16],"until":[17],"it":[18],"reaches":[19],"or":[21],"more":[22],"a":[25,74,102],"target":[26,37,80,131,151],"set.":[27],"The":[28],"time":[29],"required":[30],"for":[31,149],"to":[34,124,139,145],"reach":[35],"is":[39],"interest":[41],"understanding":[43],"convergence":[45],"Markov":[47,125],"processes,":[48,127],"as":[49,51,73,114],"well":[50],"applications":[52],"control,":[54],"machine":[55],"learning,":[56],"social":[58],"sciences.":[59],"In":[60],"this":[61,106],"paper,":[62],"we":[63],"investigate":[64],"computational":[66],"structure":[67,107],"times":[72,90,113],"function":[75],"nodes,":[81],"find":[83],"that":[84],"commute,":[86],"hitting,":[87],"cover":[89],"all":[91],"exhibit":[92],"submodular":[93],"structure,":[94],"even":[95],"nonstationary":[97],"walks.":[99],"provide":[101],"unifying":[103],"proof":[104],"by":[108],"considering":[109],"each":[110],"these":[112],"special":[115],"cases":[116],"stopping":[118],"times.":[119],"generalize":[121],"our":[122],"framework":[123],"decision":[126],"sets":[132],"control":[134],"policies":[135],"are":[136,155],"jointly":[137],"chosen":[138],"minimize":[140],"travel":[142],"times,":[143],"leading":[144],"polynomial-time":[146],"approximation":[147],"algorithms":[148],"choosing":[150],"sets.":[152],"Our":[153],"results":[154],"validated":[156],"through":[157],"numerical":[158],"study.":[159]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
