{"id":"https://openalex.org/W2089567775","doi":"https://doi.org/10.1142/s1793830909000403","title":"COMPUTING STEINER POINTS AND PROBABILITY STEINER POINTS IN \u2113<sub>1</sub> AND \u2113<sub>2</sub> METRIC SPACES","display_name":"COMPUTING STEINER POINTS AND PROBABILITY STEINER POINTS IN \u2113<sub>1</sub> AND \u2113<sub>2</sub> METRIC SPACES","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2089567775","doi":"https://doi.org/10.1142/s1793830909000403","mag":"2089567775"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830909000403","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000403","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and 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/A5054154444","display_name":"Jia Weng","orcid":"https://orcid.org/0000-0002-6976-2375"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"J. F. WENG","raw_affiliation_strings":["Department of Mechanical Engineering, The University of Melbourne, Australia","Department of Mechanical Engineering, The University Of Melbourne, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, The University of Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mechanical Engineering, The University Of Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017329457","display_name":"Iven Mareels","orcid":"https://orcid.org/0000-0002-9832-5959"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"I. MAREELS","raw_affiliation_strings":["Melbourne School of Engineering, The University of Melbourne, Australia"],"affiliations":[{"raw_affiliation_string":"Melbourne School of Engineering, The University of Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065822881","display_name":"D. A. Thomas","orcid":"https://orcid.org/0000-0002-8141-3362"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"D. A. THOMAS","raw_affiliation_strings":["Department of Mechanical Engineering, The University of Melbourne, Australia","Department of Mechanical Engineering, The University Of Melbourne, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, The University of Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Mechanical Engineering, The University Of Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054154444"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":0.2991,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62777735,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"01","issue":"04","first_page":"541","last_page":"554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.9869999885559082,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.9833174347877502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7514877319335938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7492501139640808},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5256052017211914},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.516390860080719},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.49828100204467773},{"id":"https://openalex.org/keywords/k-minimum-spanning-tree","display_name":"k-minimum spanning tree","score":0.48641133308410645},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.46776527166366577},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4441407024860382},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4420815408229828},{"id":"https://openalex.org/keywords/steiner-system","display_name":"Steiner system","score":0.43536412715911865},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.22010251879692078},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.07732915878295898},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07488298416137695}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.9833174347877502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7514877319335938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7492501139640808},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5256052017211914},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.516390860080719},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.49828100204467773},{"id":"https://openalex.org/C202750272","wikidata":"https://www.wikidata.org/wiki/Q6322849","display_name":"k-minimum spanning tree","level":5,"score":0.48641133308410645},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.46776527166366577},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4441407024860382},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4420815408229828},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.43536412715911865},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.22010251879692078},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.07732915878295898},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07488298416137695},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830909000403","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000403","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W179792009","https://openalex.org/W1600385162","https://openalex.org/W2018943178","https://openalex.org/W2094722234","https://openalex.org/W4242484817"],"related_works":["https://openalex.org/W974563791","https://openalex.org/W2739242419","https://openalex.org/W1595291551","https://openalex.org/W4244816249","https://openalex.org/W2183636263","https://openalex.org/W2999680961","https://openalex.org/W1992362850","https://openalex.org/W2050428285","https://openalex.org/W2096702260","https://openalex.org/W2089567775"],"abstract_inverted_index":{"The":[0,98],"Steiner":[1,20,32,60,64,78,83,102,108,120,124,135,139,147,151,174,182],"tree":[2,33,79,84,90,104,175,186],"problem":[3,10,34,47],"is":[4,67,80],"a":[5,14,19,24,56,81,95,101,106,172],"well":[6],"known":[7],"network":[8,17],"optimization":[9],"which":[11],"asks":[12],"for":[13,145],"connected":[15],"minimum":[16,21,61,65,103],"(called":[18],"tree)":[22,109],"spanning":[23],"given":[25,36,115],"point":[26,116,183],"set":[27,117],"N.":[28],"In":[29,127],"the":[30,35,40,46,70,73,89,114,132,143,169,180,185],"original":[31],"points":[37,87,99,121,125,136,148,152,178],"lie":[38],"in":[39,51,72,88,94,100,113,153,184,194],"Euclidean":[41],"plane":[42],"or":[43],"space,":[44],"and":[45,137,141,149,157,179],"has":[48],"many":[49],"variants":[50],"different":[52],"applications":[53],"now.":[54],"Recently":[55],"new":[57],"type":[58],"of":[59,75,134,171],"tree,":[62,66],"probability":[63,82,92,107,123,138,150,173,181],"introduced":[68],"by":[69,165],"authors":[71],"study":[74],"phylogenies.":[76],"A":[77],"if":[85],"all":[86],"are":[91,111,118,187],"vectors":[93],"vector":[96],"space.":[97],"(or":[105,122],"that":[110,168],"not":[112],"called":[119],"respectively).":[126],"this":[128],"paper":[129],"we":[130,163],"investigate":[131],"properties":[133],"points,":[140],"derive":[142],"formulae":[144],"computing":[146],"\u2113":[154,158],"1":[155],"-":[156],"2":[159],"-metric":[160],"spaces.":[161],"Moreover,":[162],"show":[164],"an":[166],"example":[167],"length":[170],"on":[176],"3":[177],"smooth":[188],"functions":[189],"with":[190],"respect":[191],"to":[192],"p":[193],"d-space.":[195]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
