{"id":"https://openalex.org/W3157737014","doi":"https://doi.org/10.1145/3406325.3451062","title":"Stronger bounds for weak epsilon-nets in higher dimensions","display_name":"Stronger bounds for weak epsilon-nets in higher dimensions","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3157737014","doi":"https://doi.org/10.1145/3406325.3451062","mag":"3157737014"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451062","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.12654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014573012","display_name":"Natan Rubin","orcid":"https://orcid.org/0000-0002-7463-6728"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Natan Rubin","raw_affiliation_strings":["Ben-Gurion University of the Negev, Israel","Ben\u2010Gurion University of the Negev, Israel"],"raw_orcid":"https://orcid.org/0000-0002-7463-6728","affiliations":[{"raw_affiliation_string":"Ben-Gurion University of the Negev, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Ben\u2010Gurion University of the Negev, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014573012"],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":0.4206,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68136064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"989","last_page":"1002"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/cardinality","display_name":"Cardinality (data modeling)","score":0.8608168363571167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7610569000244141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.67357337474823},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6649874448776245},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5349845290184021},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.49376019835472107},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.43082308769226074},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16991183161735535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1590527594089508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0402313768863678}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8608168363571167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7610569000244141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.67357337474823},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6649874448776245},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5349845290184021},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.49376019835472107},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.43082308769226074},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16991183161735535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1590527594089508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0402313768863678},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3406325.3451062","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2104.12654","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.12654","pdf_url":"https://arxiv.org/pdf/2104.12654","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":"mag:3157737014","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2104.12654.pdf","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.2104.12654","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.12654","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:2104.12654","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.12654","pdf_url":"https://arxiv.org/pdf/2104.12654","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":[{"id":"https://openalex.org/G1970926230","display_name":null,"funder_award_id":"678765","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3157737014.pdf","grobid_xml":"https://content.openalex.org/works/W3157737014.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W54178075","https://openalex.org/W1509442273","https://openalex.org/W1599814229","https://openalex.org/W1664849218","https://openalex.org/W1964691748","https://openalex.org/W1983132041","https://openalex.org/W1992800043","https://openalex.org/W1995671037","https://openalex.org/W1999396007","https://openalex.org/W2002642771","https://openalex.org/W2005411543","https://openalex.org/W2008581147","https://openalex.org/W2009545408","https://openalex.org/W2011387411","https://openalex.org/W2011451001","https://openalex.org/W2018858611","https://openalex.org/W2020799482","https://openalex.org/W2022671649","https://openalex.org/W2025809050","https://openalex.org/W2027039181","https://openalex.org/W2028747718","https://openalex.org/W2028801888","https://openalex.org/W2029272180","https://openalex.org/W2029538739","https://openalex.org/W2034838716","https://openalex.org/W2038111318","https://openalex.org/W2043060962","https://openalex.org/W2046487802","https://openalex.org/W2050459520","https://openalex.org/W2054459484","https://openalex.org/W2054680493","https://openalex.org/W2058787216","https://openalex.org/W2070611841","https://openalex.org/W2080052061","https://openalex.org/W2095555596","https://openalex.org/W2102115128","https://openalex.org/W2115730400","https://openalex.org/W2119142868","https://openalex.org/W2120948000","https://openalex.org/W2124187705","https://openalex.org/W2135079532","https://openalex.org/W2166961358","https://openalex.org/W2167816765","https://openalex.org/W2567966754","https://openalex.org/W2589206893","https://openalex.org/W2885976126","https://openalex.org/W2919703939","https://openalex.org/W2962743131","https://openalex.org/W2962915177","https://openalex.org/W2963084798","https://openalex.org/W2984826995","https://openalex.org/W2993416013","https://openalex.org/W3009933977","https://openalex.org/W3041766665","https://openalex.org/W3098403304","https://openalex.org/W4235042979","https://openalex.org/W4253015087","https://openalex.org/W4254343065","https://openalex.org/W6601348183"],"related_works":["https://openalex.org/W1587763145","https://openalex.org/W2952340676","https://openalex.org/W3178525333","https://openalex.org/W2597464241","https://openalex.org/W2124187705","https://openalex.org/W1574069817","https://openalex.org/W2902212065","https://openalex.org/W2950034637","https://openalex.org/W100082232","https://openalex.org/W345958763","https://openalex.org/W2737803646","https://openalex.org/W2538091669","https://openalex.org/W2970165664","https://openalex.org/W2588668853","https://openalex.org/W2418091306","https://openalex.org/W2952165733","https://openalex.org/W3167374180","https://openalex.org/W2590927133","https://openalex.org/W2952859539","https://openalex.org/W3137805850"],"abstract_inverted_index":{"Given":[0],"a":[1,16],"finite":[2],"point":[3],"set":[4,24],"P":[5],"in":[6],"\u211dd,":[7],"and":[8],">0":[9],"we":[10],"say":[11],"that":[12],"N\u2286":[13],"\u211dd":[14],"is":[15],"weak":[17],"-net":[18],"if":[19],"it":[20],"pierces":[21],"every":[22],"convex":[23],"K":[25],"with":[26],"|K\u2229":[27],"P|\u2265":[28],"\u0454":[29],"|P|.":[30]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}