{"id":"https://openalex.org/W2157507456","doi":"https://doi.org/10.1142/s0218195994000033","title":"Maximal Balls of Linearly Separable Sets","display_name":"Maximal Balls of Linearly Separable Sets","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2157507456","doi":"https://doi.org/10.1142/s0218195994000033","mag":"2157507456"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195994000033","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195994000033","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","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/A5046887194","display_name":"Vijay Srinivasan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"VIJAY SRINIVASAN","raw_affiliation_strings":["Manufacturing Research Department, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA"],"affiliations":[{"raw_affiliation_string":"Manufacturing Research Department, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109358421","display_name":"Lee R. Nackman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"LEE R. NACKMAN","raw_affiliation_strings":["Computer Science Department, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046887194"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5307,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68785536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"04","issue":"01","first_page":"25","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9955999851226807,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.885590672492981},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8370455503463745},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6171226501464844},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.574087917804718},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5441452264785767},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5224310755729675},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.5135414600372314},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4894391596317291},{"id":"https://openalex.org/keywords/discrete-geometry","display_name":"Discrete geometry","score":0.47951486706733704},{"id":"https://openalex.org/keywords/simplicial-approximation-theorem","display_name":"Simplicial approximation theorem","score":0.4432961046695709},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3443256616592407},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3369365334510803},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3148365020751953},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2443585991859436},{"id":"https://openalex.org/keywords/simplicial-set","display_name":"Simplicial set","score":0.06404989957809448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.885590672492981},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8370455503463745},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6171226501464844},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.574087917804718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5441452264785767},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5224310755729675},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.5135414600372314},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4894391596317291},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.47951486706733704},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.4432961046695709},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3443256616592407},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3369365334510803},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3148365020751953},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2443585991859436},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.06404989957809448},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195994000033","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195994000033","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2351580801","https://openalex.org/W2739428663","https://openalex.org/W2042426695","https://openalex.org/W2054736321","https://openalex.org/W1837161170","https://openalex.org/W1622886920","https://openalex.org/W2953288563","https://openalex.org/W1898853828","https://openalex.org/W4302787041","https://openalex.org/W4321149742"],"abstract_inverted_index":{"Maximal":[0],"balls":[1],"(and":[2],"the":[3,19,23,34],"associated":[4],"maximal":[5,39],"spheres)":[6],"between":[7,50],"sets":[8,51],"arise":[9],"naturally":[10],"in":[11,46,52,60],"several":[12],"areas":[13],"of":[14,38,63,66],"computational":[15],"geometry":[16],"such":[17],"as":[18],"Voronoi":[20],"diagram":[21],"and":[22,30,36],"symmetric":[24],"axis":[25],"transform.":[26],"We":[27],"give":[28],"necessary":[29],"sufficient":[31],"conditions":[32],"for":[33],"existence":[35],"uniqueness":[37],"spheres":[40],"to":[41],"pass":[42],"through":[43],"specified":[44],"points":[45],"a":[47],"linear":[48],"separator":[49],"E":[53],"d":[54],".":[55],"These":[56],"results":[57],"are":[58],"applicable":[59],"certain":[61],"problems":[62],"simplicial":[64],"decomposition":[65],"domains.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}