{"id":"https://openalex.org/W2164732056","doi":"https://doi.org/10.1007/s10898-012-9967-3","title":"Approximations for two variants of the Steiner tree problem in the Euclidean plane $${\\mathbb{R}^2}$$","display_name":"Approximations for two variants of the Steiner tree problem in the Euclidean plane $${\\mathbb{R}^2}$$","publication_year":2012,"publication_date":"2012-08-23","ids":{"openalex":"https://openalex.org/W2164732056","doi":"https://doi.org/10.1007/s10898-012-9967-3","mag":"2164732056"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-012-9967-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9967-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","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/A5018144399","display_name":"Jianping Li","orcid":"https://orcid.org/0000-0003-1508-1440"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianping Li","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034106374","display_name":"Haiyan Wang","orcid":"https://orcid.org/0000-0002-5212-5687"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiyan Wang","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100899236","display_name":"Binchao Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binchao Huang","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004025610","display_name":"Junran Lichen","orcid":"https://orcid.org/0000-0003-1385-8957"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junran Lichen","raw_affiliation_strings":["School of Economics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Economics, Yunnan University, Kunming, 650091, Yunnan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I189210763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018144399"],"corresponding_institution_ids":["https://openalex.org/I189210763"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16681963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T14117","display_name":"Integrated Circuits and Semiconductor Failure Analysis","score":0.989799976348877,"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":0.9471491575241089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8588047623634338},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8232156038284302},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6083109378814697},{"id":"https://openalex.org/keywords/steiner-system","display_name":"Steiner system","score":0.4555753767490387},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43923333287239075},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.41200166940689087},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38177788257598877},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1667151153087616}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.9471491575241089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8588047623634338},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8232156038284302},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6083109378814697},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.4555753767490387},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43923333287239075},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.41200166940689087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38177788257598877},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1667151153087616}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-012-9967-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9967-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:57:y:2013:i:3:p:783-801","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-012-9967-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1525228936","https://openalex.org/W1543735555","https://openalex.org/W1543921836","https://openalex.org/W1984458273","https://openalex.org/W1990313671","https://openalex.org/W2011039300","https://openalex.org/W2024833542","https://openalex.org/W2042492403","https://openalex.org/W2052064586","https://openalex.org/W2053913299","https://openalex.org/W2060380213","https://openalex.org/W2069002708","https://openalex.org/W2069323107","https://openalex.org/W2086709935","https://openalex.org/W2087675574","https://openalex.org/W2114753568","https://openalex.org/W2122877872","https://openalex.org/W2128456629","https://openalex.org/W2145965938","https://openalex.org/W2611804663","https://openalex.org/W2988480584","https://openalex.org/W4230573295","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2011703460","https://openalex.org/W1992380975","https://openalex.org/W2080581853","https://openalex.org/W3201893458","https://openalex.org/W2025658531","https://openalex.org/W2325263694","https://openalex.org/W2500374022","https://openalex.org/W2003806381","https://openalex.org/W2090486508","https://openalex.org/W2051685615"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}