{"id":"https://openalex.org/W2069172499","doi":"https://doi.org/10.1007/s00454-002-2756-x","title":"Geometric Optimization Problems Likely Not Contained in $$\\mathbb{A}\\mathbb{P}\\mathbb{X}$$","display_name":"Geometric Optimization Problems Likely Not Contained in $$\\mathbb{A}\\mathbb{P}\\mathbb{X}$$","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W2069172499","doi":"https://doi.org/10.1007/s00454-002-2756-x","mag":"2069172499"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-002-2756-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2756-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2756-x.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/s00454-002-2756-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097431508","display_name":"Brieden","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Brieden","raw_affiliation_strings":["Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, D-80290 Munich, Germany brieden@ma.tum.de, Germany","Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, D-80290 Munich, Germany brieden@ma.tum.de, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, D-80290 Munich, Germany brieden@ma.tum.de, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, D-80290 Munich, Germany brieden@ma.tum.de, Germany#TAB#","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5097431508"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5656,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.81826654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"2","first_page":"201","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980000257492065,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9904000163078308,"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/polytope","display_name":"Polytope","score":0.9342207908630371},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8267676830291748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7712625861167908},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5776061415672302},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48988932371139526},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4764305055141449},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.352740079164505},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15135785937309265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10408899188041687}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9342207908630371},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8267676830291748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7712625861167908},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5776061415672302},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48988932371139526},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4764305055141449},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.352740079164505},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15135785937309265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10408899188041687},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-002-2756-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2756-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2756-x.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"}],"best_oa_location":{"id":"doi:10.1007/s00454-002-2756-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2756-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2756-x.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/W2069172499.pdf","grobid_xml":"https://content.openalex.org/works/W2069172499.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1511716344","https://openalex.org/W1934904397","https://openalex.org/W1975360289","https://openalex.org/W1999351098","https://openalex.org/W2013821228","https://openalex.org/W2016232593","https://openalex.org/W2019886197","https://openalex.org/W2022029673","https://openalex.org/W2025190766","https://openalex.org/W2090863037","https://openalex.org/W2221440952","https://openalex.org/W2912000438","https://openalex.org/W4249532171"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W3103454236","https://openalex.org/W1854082044","https://openalex.org/W3169007055"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"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":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}