{"id":"https://openalex.org/W2125028780","doi":"https://doi.org/10.1007/s00454-001-0006-2","title":"A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization","display_name":"A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization","publication_year":2001,"publication_date":"2001-04-01","ids":{"openalex":"https://openalex.org/W2125028780","doi":"https://doi.org/10.1007/s00454-001-0006-2","mag":"2125028780"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-001-0006-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-001-0006-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-001-0006-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-001-0006-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017124525","display_name":"Bernd G\u00e4rtner","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"B. G\u00e4rtner","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\{gaertner,emo\\}@inf.ethz.ch, Switzerland","Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\\\{gaertner,emo\\\\}@inf.ethz.ch, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\{gaertner,emo\\}@inf.ethz.ch, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\\\{gaertner,emo\\\\}@inf.ethz.ch, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107336010","display_name":"Emo Welzl","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"E. Welzl","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\{gaertner,emo\\}@inf.ethz.ch, Switzerland","Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\\\{gaertner,emo\\\\}@inf.ethz.ch, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\{gaertner,emo\\}@inf.ethz.ch, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, ETH Z\u00fcrich, ETH Zentrum, CH-8092 Z\u00fcrich, Switzerland \\\\{gaertner,emo\\\\}@inf.ethz.ch, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017124525"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.1842,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.89395929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"4","first_page":"569","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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/T11106","display_name":"Data Management and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.754100501537323},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5635485053062439},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.544222354888916},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5055179595947266},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5040684938430786},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.45816925168037415},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4254586100578308},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27363771200180054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19176927208900452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.754100501537323},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5635485053062439},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.544222354888916},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5055179595947266},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5040684938430786},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.45816925168037415},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4254586100578308},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27363771200180054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19176927208900452},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-001-0006-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-001-0006-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-001-0006-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.4386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.4386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.ethz.ch/personal/gaertner/texts/own_work/sampling_final.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-001-0006-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-001-0006-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-001-0006-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2125028780.pdf","grobid_xml":"https://content.openalex.org/works/W2125028780.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1496278954","https://openalex.org/W1533912360","https://openalex.org/W1575669909","https://openalex.org/W1593563200","https://openalex.org/W1595208863","https://openalex.org/W1607203414","https://openalex.org/W1646289414","https://openalex.org/W1788997585","https://openalex.org/W1789652828","https://openalex.org/W1970198959","https://openalex.org/W1980514846","https://openalex.org/W1981732464","https://openalex.org/W1985372427","https://openalex.org/W1987752344","https://openalex.org/W1990970199","https://openalex.org/W1997964544","https://openalex.org/W1998909289","https://openalex.org/W2010790640","https://openalex.org/W2014574315","https://openalex.org/W2040103897","https://openalex.org/W2057399436","https://openalex.org/W2057512681","https://openalex.org/W2058432138","https://openalex.org/W2064525551","https://openalex.org/W2067631433","https://openalex.org/W2138304862","https://openalex.org/W2149906774","https://openalex.org/W2152479402","https://openalex.org/W2168047345","https://openalex.org/W2295428206","https://openalex.org/W2752885492","https://openalex.org/W4210521336","https://openalex.org/W4210791125","https://openalex.org/W4231916799","https://openalex.org/W4240756993","https://openalex.org/W7029321148"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W2949964783","https://openalex.org/W4308265086","https://openalex.org/W2227962536","https://openalex.org/W4293582632","https://openalex.org/W2072760177","https://openalex.org/W2159809789","https://openalex.org/W4298954232"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}