{"id":"https://openalex.org/W2104397519","doi":"https://doi.org/10.37236/2921","title":"The Capture Time of the Hypercube","display_name":"The Capture Time of the Hypercube","publication_year":2013,"publication_date":"2013-04-30","ids":{"openalex":"https://openalex.org/W2104397519","doi":"https://doi.org/10.37236/2921","mag":"2104397519"},"language":"en","primary_location":{"id":"doi:10.37236/2921","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2921","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p24/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p24/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082423050","display_name":"Anthony Bonato","orcid":"https://orcid.org/0000-0003-3969-5412"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anthony Bonato","raw_affiliation_strings":["(Ryerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Ryerson University","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090880856","display_name":"Przemys\u0142aw Gordinowicz","orcid":"https://orcid.org/0000-0001-9843-3928"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA","PL"],"is_corresponding":false,"raw_author_name":"Przemys\u0142aw Gordinowicz","raw_affiliation_strings":["Department of Mathematics Ryerson University Toronto, ON, Canada","Institute of Mathematics Technical University of Lodz L\u00f3d\u017a, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Ryerson University Toronto, ON, Canada","institution_ids":["https://openalex.org/I530967"]},{"raw_affiliation_string":"Institute of Mathematics Technical University of Lodz L\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I188884621","https://openalex.org/I4210137370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066916191","display_name":"Bill Kinnersley","orcid":null},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA","PL"],"is_corresponding":false,"raw_author_name":"Bill Kinnersley","raw_affiliation_strings":["Department of Mathematics Ryerson University Toronto, ON, Canada","Institute of Mathematics Technical University of Lodz L\u00f3d\u017a, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Ryerson University Toronto, ON, Canada","institution_ids":["https://openalex.org/I530967"]},{"raw_affiliation_string":"Institute of Mathematics Technical University of Lodz L\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I188884621","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079925942","display_name":"Pawe\u0142 Pra\u0142at","orcid":"https://orcid.org/0000-0001-9176-8493"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Pra\u0142at","raw_affiliation_strings":["Department of Mathematics\r\nRyerson University","Department of Mathematics#R##N#Ryerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nRyerson University","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#Ryerson University","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1902,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.81526277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"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":0.9991999864578247,"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":0.9991999864578247,"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/T12288","display_name":"Optimization and Search Problems","score":0.9983999729156494,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9969000220298767,"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/hypercube","display_name":"Hypercube","score":0.9304352402687073},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7075831294059753},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5945250391960144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5889888405799866},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37541908025741577}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.9304352402687073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7075831294059753},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5945250391960144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5889888405799866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37541908025741577}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/2921","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2921","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p24/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.719.5500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.719.5500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ryerson.ca/%7Eabonato/papers/capturetime_hypercube1123_b.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.6622","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.6622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1308.3354.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/2921","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2921","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p24/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6700000166893005,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2104397519.pdf","grobid_xml":"https://content.openalex.org/works/W2104397519.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W280278083","https://openalex.org/W1998631802","https://openalex.org/W2028400828","https://openalex.org/W2035417355","https://openalex.org/W2043312585","https://openalex.org/W2046635105","https://openalex.org/W2063843010","https://openalex.org/W2130202938","https://openalex.org/W2171304259","https://openalex.org/W2398221731","https://openalex.org/W2499688774","https://openalex.org/W2963514297","https://openalex.org/W2963612420","https://openalex.org/W3139940246","https://openalex.org/W3148190347","https://openalex.org/W4301352371","https://openalex.org/W6610130217","https://openalex.org/W6649905890","https://openalex.org/W6657531994","https://openalex.org/W6659349814","https://openalex.org/W6662295107","https://openalex.org/W6673554864","https://openalex.org/W6679340559"],"related_works":["https://openalex.org/W2916710807","https://openalex.org/W4286907761","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W2371629703","https://openalex.org/W2097769911","https://openalex.org/W2774705104","https://openalex.org/W72835634","https://openalex.org/W2122785676"],"abstract_inverted_index":{"In":[0],"the":[1,7,14,21,25,33,37,52,56,59],"game":[2],"of":[3,10,17,36,58],"Cops":[4],"and":[5],"Robbers,":[6],"capture":[8,24,34],"time":[9,35],"a":[11,47],"graph":[12],"is":[13,40],"minimum":[15],"number":[16],"moves":[18],"needed":[19],"by":[20],"cops":[22],"to":[23],"robber,":[26],"assuming":[27],"optimal":[28],"play.":[29],"We":[30],"prove":[31],"that":[32],"$n$-dimensional":[38],"hypercube":[39],"$\\Theta":[41],"(n\\ln":[42],"n)$.":[43],"Our":[44],"methods":[45],"include":[46],"novel":[48],"randomized":[49],"strategy":[50],"for":[51],"players,":[53],"which":[54],"involves":[55],"analysis":[57],"coupon-collector":[60],"problem.":[61]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}