{"id":"https://openalex.org/W4306177426","doi":"https://doi.org/10.48550/arxiv.2210.05982","title":"A nearly optimal randomized algorithm for explorable heap selection","display_name":"A nearly optimal randomized algorithm for explorable heap selection","publication_year":2022,"publication_date":"2022-10-12","ids":{"openalex":"https://openalex.org/W4306177426","doi":"https://doi.org/10.48550/arxiv.2210.05982"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2210.05982","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.05982","pdf_url":"https://arxiv.org/pdf/2210.05982","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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2210.05982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086943500","display_name":"Sander Borst","orcid":"https://orcid.org/0000-0003-4001-6675"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borst, Sander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044591096","display_name":"Daniel Dadush","orcid":"https://orcid.org/0000-0001-5577-5012"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dadush, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034599189","display_name":"Sophie Huiberts","orcid":"https://orcid.org/0000-0003-2633-014X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huiberts, Sophie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032576640","display_name":"Danish Kashaev","orcid":"https://orcid.org/0000-0002-7999-4989"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kashaev, Danish","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":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9991000294685364,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991000294685364,"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/T12288","display_name":"Optimization and Search Problems","score":0.9807000160217285,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9675999879837036,"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":0.7012263536453247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.664310872554779},{"id":"https://openalex.org/keywords/heap","display_name":"Heap (data structure)","score":0.6306067109107971},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.6279881596565247},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6139132976531982},{"id":"https://openalex.org/keywords/traverse","display_name":"Traverse","score":0.5205893516540527},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.49025657773017883},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.48161834478378296},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4718363583087921},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4662930369377136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.424316942691803},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.36989349126815796},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1242825984954834}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7012263536453247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.664310872554779},{"id":"https://openalex.org/C134757568","wikidata":"https://www.wikidata.org/wiki/Q274089","display_name":"Heap (data structure)","level":2,"score":0.6306067109107971},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.6279881596565247},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6139132976531982},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.5205893516540527},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.49025657773017883},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.48161834478378296},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4718363583087921},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4662930369377136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.424316942691803},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.36989349126815796},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1242825984954834},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2210.05982","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.05982","pdf_url":"https://arxiv.org/pdf/2210.05982","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:cwi.nl:32263","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/32263","pdf_url":"https://ir.cwi.nl/pub/32263/32263.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"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":"info:eu-repo/semantics/other"},{"id":"pmh:oai:dspace.library.uu.nl:1874/474032","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/474032","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2210.05982","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2210.05982","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2210.05982","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2210.05982","pdf_url":"https://arxiv.org/pdf/2210.05982","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3091917984","https://openalex.org/W4287644226","https://openalex.org/W2056975861","https://openalex.org/W2363556447","https://openalex.org/W2089900921","https://openalex.org/W2501849745","https://openalex.org/W2011933350","https://openalex.org/W1510719821","https://openalex.org/W2093708041","https://openalex.org/W2041182800"],"abstract_inverted_index":{"Explorable":[0],"heap":[1],"selection":[2],"is":[3,37,146],"the":[4,8,26,32,35,40,45,65,110,117,134,137],"problem":[5,53,135],"of":[6,34,119,140],"selecting":[7],"$n$th":[9],"smallest":[10],"value":[11],"in":[12,44,136],"a":[13,58,96],"binary":[14,29],"heap.":[15],"The":[16],"key":[17],"values":[18],"can":[19],"only":[20],"be":[21],"accessed":[22],"by":[23,39,71],"traversing":[24],"through":[25],"underlying":[27],"infinite":[28],"tree,":[30],"and":[31,74,81,89],"complexity":[33],"algorithm":[36,67,99,131,145],"measured":[38],"total":[41],"distance":[42],"traveled":[43],"tree":[46],"(each":[47],"edge":[48],"has":[49],"unit":[50],"cost).":[51],"This":[52],"was":[54],"originally":[55],"proposed":[56],"as":[57],"model":[59],"to":[60],"study":[61],"search":[62],"strategies":[63],"for":[64,129],"branch-and-bound":[66],"with":[68,100],"storage":[69],"restrictions":[70],"Karp,":[72],"Saks":[73],"Widgerson":[75],"(FOCS":[76],"'86),":[77],"who":[78],"gave":[79],"deterministic":[80],"randomized":[82,98,113],"$n\\cdot":[83],"\\exp(O(\\sqrt{\\log{n}}))$":[84],"time":[85,102,115],"algorithms":[86],"using":[87,104],"$O(\\log(n)^{2.5})$":[88],"$O(\\sqrt{\\log":[90],"n})$":[91],"space":[92,122],"respectively.":[93],"We":[94,124],"present":[95],"new":[97],"running":[101,114],"$O(n\\log(n)^3)$":[103],"$O(\\log":[105],"n)$":[106],"space,":[107,141],"substantially":[108],"improving":[109],"previous":[111],"best":[112],"at":[116],"expense":[118],"slightly":[120],"increased":[121],"usage.":[123],"also":[125],"show":[126],"an":[127],"$\u03a9(\\log(n)n/\\log(\\log(n)))$":[128],"any":[130],"that":[132,143],"solves":[133],"same":[138],"amount":[139],"indicating":[142],"our":[144],"nearly":[147],"optimal.":[148]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
