{"id":"https://openalex.org/W2587329907","doi":"https://doi.org/10.1007/s00493-017-3564-5","title":"A Simple Proof of Optimal Epsilon Nets","display_name":"A Simple Proof of Optimal Epsilon Nets","publication_year":2017,"publication_date":"2017-06-13","ids":{"openalex":"https://openalex.org/W2587329907","doi":"https://doi.org/10.1007/s00493-017-3564-5","mag":"2587329907"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-017-3564-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-017-3564-5","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01360452v1/file/simpleproofepsnets.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051793571","display_name":"Nabil H. Mustafa","orcid":"https://orcid.org/0000-0003-1046-6157"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nabil H. Mustafa","raw_affiliation_strings":["Universit\u00e9 Paris-Est Laboratoire d\u2019Informatique Gaspard-Monge, ESIEE Paris, Noisy-le-Grand, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est Laboratoire d\u2019Informatique Gaspard-Monge, ESIEE Paris, Noisy-le-Grand, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064136684","display_name":"Kunal Dutta","orcid":"https://orcid.org/0000-0003-3055-9326"},"institutions":[{"id":"https://openalex.org/I4210106545","display_name":"Research Centre Inria Sophia Antipolis - M\u00e9diterran\u00e9e","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Kunal Dutta","raw_affiliation_strings":["DataShape, INRIA Sophia Antipolis - M\u00e9diterran\u00e9e Sophia Antipolis, Valbonne, France"],"affiliations":[{"raw_affiliation_string":"DataShape, INRIA Sophia Antipolis - M\u00e9diterran\u00e9e Sophia Antipolis, Valbonne, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101861796","display_name":"Arijit Ghosh","orcid":"https://orcid.org/0000-0002-2821-265X"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Arijit Ghosh","raw_affiliation_strings":["ACM Unit, Indian Statistical Institute, Kolkata, India"],"affiliations":[{"raw_affiliation_string":"ACM Unit, Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051793571"],"corresponding_institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"],"apc_list":null,"apc_paid":null,"fwci":1.6592,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84986532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"5","first_page":"1269","last_page":"1277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"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/simple","display_name":"Simple (philosophy)","score":0.8024052977561951},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5639646053314209},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5457299947738647},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5016281604766846},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47542956471443176},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.4645853340625763},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43685194849967957},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4206390976905823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36412373185157776},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3461265563964844},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.34220588207244873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32995253801345825},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.09252214431762695},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07159411907196045}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8024052977561951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5639646053314209},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5457299947738647},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5016281604766846},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47542956471443176},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.4645853340625763},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43685194849967957},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4206390976905823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36412373185157776},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3461265563964844},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34220588207244873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32995253801345825},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.09252214431762695},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07159411907196045},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00493-017-3564-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-017-3564-5","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01360452v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01360452","pdf_url":"https://hal.science/hal-01360452v1/file/simpleproofepsnets.pdf","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":"Combinatorica, 2017, ⟨10.1007/s00493-017-3564-5⟩","raw_type":"Journal articles"},{"id":"pmh:oai:escidoc.org:escidoc:2397893","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002C-65CA-7","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01360452v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01360452","pdf_url":"https://hal.science/hal-01360452v1/file/simpleproofepsnets.pdf","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":"Combinatorica, 2017, ⟨10.1007/s00493-017-3564-5⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2587329907.pdf","grobid_xml":"https://content.openalex.org/works/W2587329907.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1518816409","https://openalex.org/W1531964914","https://openalex.org/W1550105891","https://openalex.org/W1599814229","https://openalex.org/W1623497062","https://openalex.org/W1920697702","https://openalex.org/W1971361630","https://openalex.org/W1983851263","https://openalex.org/W1986685589","https://openalex.org/W1992800043","https://openalex.org/W1995671037","https://openalex.org/W1999396007","https://openalex.org/W2013195123","https://openalex.org/W2013561419","https://openalex.org/W2020913456","https://openalex.org/W2029538739","https://openalex.org/W2050459520","https://openalex.org/W2054459484","https://openalex.org/W2058239479","https://openalex.org/W2058432138","https://openalex.org/W2064561047","https://openalex.org/W2103893986","https://openalex.org/W2119142868","https://openalex.org/W2124187705","https://openalex.org/W2127739958","https://openalex.org/W2128227281","https://openalex.org/W2167816765","https://openalex.org/W2202493075","https://openalex.org/W2274455069","https://openalex.org/W2292762267","https://openalex.org/W2481227236","https://openalex.org/W2525451309","https://openalex.org/W2538756287","https://openalex.org/W2568742159","https://openalex.org/W2592570088","https://openalex.org/W2912202394","https://openalex.org/W2951116190","https://openalex.org/W4238284510","https://openalex.org/W4241195282","https://openalex.org/W4249137521","https://openalex.org/W4254343065","https://openalex.org/W4254977685","https://openalex.org/W6712295170"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W4300101996","https://openalex.org/W2142393343","https://openalex.org/W3101625811","https://openalex.org/W2338854850"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}