{"id":"https://openalex.org/W4283805763","doi":"https://doi.org/10.1145/3476446.3536190","title":"On the Error of Random Sampling","display_name":"On the Error of Random Sampling","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283805763","doi":"https://doi.org/10.1145/3476446.3536190"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3536190","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024426907","display_name":"Apostolos Chalkis","orcid":"https://orcid.org/0000-0002-4628-1907"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]},{"id":"https://openalex.org/I4210094138","display_name":"University of West Attica","ror":"https://ror.org/00r2r5k05","country_code":"GR","type":"education","lineage":["https://openalex.org/I4210094138"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Apostolos Chalkis","raw_affiliation_strings":["GeomScale org, Athens, Greece","NKUA - National and Kapodistrian University of Athens (Athens 157 72 - Greece)"],"affiliations":[{"raw_affiliation_string":"GeomScale org, Athens, Greece","institution_ids":["https://openalex.org/I4210094138"]},{"raw_affiliation_string":"NKUA - National and Kapodistrian University of Athens (Athens 157 72 - Greece)","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036559688","display_name":"Christina Katsamaki","orcid":"https://orcid.org/0000-0002-3177-010X"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4403386633","display_name":"OURAGAN: Outils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses Applications","ror":"https://ror.org/01rrvyp50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4403386633"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christina Katsamaki","raw_affiliation_strings":["Inria Paris & IMJ-PRG, Paris, France","OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)"],"affiliations":[{"raw_affiliation_string":"Inria Paris & IMJ-PRG, Paris, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)","institution_ids":["https://openalex.org/I4403386633"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021775859","display_name":"Josu\u00e9 Tonelli-Cueto","orcid":"https://orcid.org/0000-0002-2904-1215"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4403386633","display_name":"OURAGAN: Outils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses Applications","ror":"https://ror.org/01rrvyp50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4403386633"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Josu\u00e9 Tonelli-Cueto","raw_affiliation_strings":["Inria Paris & IMJ-PRG, Paris, France","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)"],"affiliations":[{"raw_affiliation_string":"Inria Paris & IMJ-PRG, Paris, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I3017942884"]},{"raw_affiliation_string":"OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)","institution_ids":["https://openalex.org/I4403386633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024426907"],"corresponding_institution_ids":["https://openalex.org/I200777214","https://openalex.org/I4210094138"],"apc_list":null,"apc_paid":null,"fwci":0.26334776,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4714318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"273","last_page":"282"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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":0.9983999729156494,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5918183922767639},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.5795493721961975},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5355131030082703},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5293462872505188},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5285131931304932},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4898185431957245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4848000109195709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4730607271194458},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.43239057064056396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4314761161804199},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3331497311592102},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32865968346595764},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21073570847511292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11099240183830261},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10496792197227478}],"concepts":[{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5918183922767639},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.5795493721961975},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5355131030082703},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5293462872505188},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5285131931304932},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4898185431957245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4848000109195709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4730607271194458},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.43239057064056396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4314761161804199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3331497311592102},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32865968346595764},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21073570847511292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11099240183830261},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10496792197227478},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3476446.3536190","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W32980360","https://openalex.org/W115562957","https://openalex.org/W222318538","https://openalex.org/W253307310","https://openalex.org/W621546036","https://openalex.org/W1550331971","https://openalex.org/W1580003832","https://openalex.org/W1809030594","https://openalex.org/W1975010018","https://openalex.org/W1996999318","https://openalex.org/W2042908764","https://openalex.org/W2061300678","https://openalex.org/W2089603726","https://openalex.org/W2098323855","https://openalex.org/W2108077794","https://openalex.org/W2108207895","https://openalex.org/W2157878484","https://openalex.org/W2204383650","https://openalex.org/W2774779442","https://openalex.org/W2783417494","https://openalex.org/W2952111492","https://openalex.org/W2954040150","https://openalex.org/W2963110896","https://openalex.org/W3023788998","https://openalex.org/W3103907078","https://openalex.org/W4254246953","https://openalex.org/W4287760333","https://openalex.org/W4288567353","https://openalex.org/W4297812647","https://openalex.org/W4301168154"],"related_works":["https://openalex.org/W4293088233","https://openalex.org/W3152660226","https://openalex.org/W2496077116","https://openalex.org/W2900695351","https://openalex.org/W2964179321","https://openalex.org/W1986523067","https://openalex.org/W3082212156","https://openalex.org/W4388813866","https://openalex.org/W4243140484","https://openalex.org/W2379877967"],"abstract_inverted_index":{"Given":[0],"a":[1,11,19,37],"parametric":[2],"polynomial":[3],"curve":[4],"\u03b3:[a,b]":[5],"\u2192Rn,":[6],"how":[7,54],"can":[8,41],"we":[9,32,40,47,58,67,88],"sample":[10,34,66],"random":[12],"point":[13,94],"x":[14],"\u2208":[15],"im(\u03b3)":[16],"in":[17,76,82,102],"such":[18,36],"way":[20],"that":[21],"it":[22],"is":[23],"distributed":[24],"uniformly":[25],"with":[26,50],"respect":[27],"to":[28],"the":[29,51,56,61,64,93,105,108],"arc-length?":[30],"Unfortunately,":[31],"cannot":[33],"exactly":[35],"point---even":[38],"assuming":[39],"perform":[42],"exact":[43],"arithmetic":[44],"operations.":[45],"So":[46],"end":[48],"up":[49],"following":[52],"question:":[53],"does":[55],"method":[57],"choose":[59],"affect":[60],"quality":[62],"of":[63,95,97,104,107],"approximate":[65],"obtain?":[68],"In":[69,85],"practice,":[70],"there":[71,78],"are":[72,79],"many":[73],"answers.":[74],"However,":[75],"theory,":[77,99],"still":[80],"gaps":[81],"our":[83],"understanding.":[84],"this":[86,90],"paper,":[87],"address":[89],"question":[91],"from":[92],"view":[96],"complexity":[98],"providing":[100],"bounds":[101],"terms":[103],"size":[106],"desired":[109],"error.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-13T15:27:49.765798","created_date":"2022-07-06T00:00:00"}