{"id":"https://openalex.org/W2157114458","doi":"https://doi.org/10.1142/s0218195914500071","title":"HARDNESS RESULTS FOR COMPUTING OPTIMAL LOCALLY GABRIEL GRAPHS","display_name":"HARDNESS RESULTS FOR COMPUTING OPTIMAL LOCALLY GABRIEL GRAPHS","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2157114458","doi":"https://doi.org/10.1142/s0218195914500071","mag":"2157114458"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195914500071","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195914500071","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 &amp; 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/A5084909127","display_name":"Abhijeet Khopkar","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"ABHIJEET KHOPKAR","raw_affiliation_strings":["Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062650037","display_name":"Sathish Govindarajan","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"SATHISH GOVINDARAJAN","raw_affiliation_strings":["Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084909127"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22623167,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"02","first_page":"153","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9941999912261963,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.6179981231689453},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.604279637336731},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5890525579452515},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46976208686828613},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4180387854576111}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6179981231689453},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.604279637336731},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5890525579452515},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46976208686828613},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4180387854576111}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195914500071","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195914500071","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 &amp; 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":14,"referenced_works":["https://openalex.org/W1519477091","https://openalex.org/W1552092932","https://openalex.org/W1970754929","https://openalex.org/W2039111454","https://openalex.org/W2044959725","https://openalex.org/W2075105933","https://openalex.org/W2132015493","https://openalex.org/W2137045378","https://openalex.org/W2139841403","https://openalex.org/W2157737430","https://openalex.org/W2161843738","https://openalex.org/W2163227453","https://openalex.org/W2319149236","https://openalex.org/W4211205179"],"related_works":["https://openalex.org/W2359979928","https://openalex.org/W2368353614","https://openalex.org/W2390369954","https://openalex.org/W1529719486","https://openalex.org/W4232052003","https://openalex.org/W2373917503","https://openalex.org/W2906423005","https://openalex.org/W2385297469","https://openalex.org/W2001914902","https://openalex.org/W2353399380"],"abstract_inverted_index":{"Delaunay":[0,24],"and":[1,27,113],"Gabriel":[2,29,43,59],"graphs":[3,20],"are":[4,52],"widely":[5],"studied":[6],"geometric":[7,144],"proximity":[8],"structures.":[9],"Motivated":[10],"by":[11],"applications":[12],"in":[13,46,54,95],"wireless":[14],"routing,":[15],"relaxed":[16],"versions":[17],"of":[18,38,93],"these":[19],"known":[21],"as":[22],"Locally":[23,28,42],"Graphs":[25,30,44],"(LDGs)":[26],"(LGGs)":[31],"were":[32],"proposed.":[33],"We":[34,98,116],"propose":[35],"another":[36],"generalization":[37],"LGGs":[39],"called":[40],"Generalized":[41],"(GLGGs)":[45],"the":[47,55,96],"context":[48],"when":[49],"certain":[50],"edges":[51],"forbidden":[53],"graph.":[56,97],"Unlike":[57],"a":[58,69,91,107,124,142,150],"Graph,":[60],"there":[61],"is":[62,76,111,132,149],"no":[63,74],"unique":[64],"LGG":[65,122],"or":[66,79],"GLGG":[67,105],"for":[68,106],"given":[70,108,125,143],"point":[71,126],"set":[72,127],"because":[73],"edge":[75,103],"necessarily":[77],"included":[78],"excluded.":[80],"This":[81],"property":[82],"allows":[83],"us":[84],"to":[85,139],"choose":[86],"an":[87,102,121,137],"LGG/GLGG":[88],"that":[89,100,119],"optimizes":[90],"parameter":[92],"interest":[94],"show":[99,118],"computing":[101,120],"maximum":[104],"problem":[109],"instance":[110],"NP-hard":[112],"also":[114,117],"APX-hard.":[115],"on":[123],"with":[128],"dilation":[129],"\u2264":[130],"k":[131],"NP-hard.":[133],"Finally,":[134],"we":[135],"give":[136],"algorithm":[138],"verify":[140],"whether":[141],"graph":[145],"G":[146],"=":[147],"(V,E)":[148],"valid":[151],"LGG.":[152]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
