{"id":"https://openalex.org/W2024331629","doi":"https://doi.org/10.1007/s004530010005","title":"A Strong and Easily Computable Separation Bound for Arithmetic Expressions Involving Radicals","display_name":"A Strong and Easily Computable Separation Bound for Arithmetic Expressions Involving Radicals","publication_year":2000,"publication_date":"2000-05-01","ids":{"openalex":"https://openalex.org/W2024331629","doi":"https://doi.org/10.1007/s004530010005","mag":"2024331629"},"language":"en","primary_location":{"id":"doi:10.1007/s004530010005","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004530010005","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"type":"article","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/A5029371878","display_name":"Christoph Burnikel","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"C. Burnikel","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112284215","display_name":"Rudolf Fleischer","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R. Fleischer","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010961023","display_name":"Kurt Mehlhorn","orcid":"https://orcid.org/0000-0003-4020-4334"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"K. Mehlhorn","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005637149","display_name":"Stefan Schirra","orcid":"https://orcid.org/0009-0006-5928-1494"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. Schirra","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany. burnikel@mpi-sb.mpg.de, rudolf@mpi-sb.mpg.de, mehlhorn@mpi-sb.mpg.de, stschirr@mpi-sb.mpg.de., , , , , , DE","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029371878"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210109712"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.1529,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.95686854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"1","first_page":"87","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9952999949455261,"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/T10126","display_name":"Logic, programming, and type systems","score":0.982699990272522,"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/mathematics","display_name":"Mathematics","score":0.7272288203239441},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.674637496471405},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6673074960708618},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6091023683547974},{"id":"https://openalex.org/keywords/operand","display_name":"Operand","score":0.597646176815033},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5906274914741516},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5169086456298828},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.4908950924873352},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.43800824880599976},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4275780916213989},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1684063971042633},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12609604001045227},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06912600994110107},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04798075556755066}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7272288203239441},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.674637496471405},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6673074960708618},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6091023683547974},{"id":"https://openalex.org/C55526617","wikidata":"https://www.wikidata.org/wiki/Q719375","display_name":"Operand","level":2,"score":0.597646176815033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5906274914741516},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5169086456298828},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.4908950924873352},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.43800824880599976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4275780916213989},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1684063971042633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12609604001045227},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06912600994110107},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04798075556755066},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s004530010005","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004530010005","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:edoc.mpg.de:344440","is_oa":false,"landing_page_url":"http://edoc.mpg.de/344440","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"Algorithmica, v.27, 87-99 (2000)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_1330790","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-333A-B","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1481724961","https://openalex.org/W1516027685","https://openalex.org/W1544964545","https://openalex.org/W1552350973","https://openalex.org/W1562798476","https://openalex.org/W1575869015","https://openalex.org/W1815267262","https://openalex.org/W2043552663","https://openalex.org/W2124925673","https://openalex.org/W2154184839","https://openalex.org/W2156153879"],"related_works":["https://openalex.org/W2556282987","https://openalex.org/W1533508804","https://openalex.org/W2050923821","https://openalex.org/W1970370079","https://openalex.org/W2333680585","https://openalex.org/W2098637578","https://openalex.org/W1999746819","https://openalex.org/W1996625680","https://openalex.org/W4378651692","https://openalex.org/W2046228374"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
