{"id":"https://openalex.org/W2062191077","doi":"https://doi.org/10.1007/bf02189328","title":"Minimum steiner trees in normed planes","display_name":"Minimum steiner trees in normed planes","publication_year":1993,"publication_date":"1993-04-01","ids":{"openalex":"https://openalex.org/W2062191077","doi":"https://doi.org/10.1007/bf02189328","mag":"2062191077"},"language":"en","primary_location":{"id":"doi:10.1007/bf02189328","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02189328","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02189328.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 &amp; 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/BF02189328.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037860988","display_name":"Ding\u2010Zhu Du","orcid":"https://orcid.org/0000-0002-7345-2185"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Ding-Zhu Du","raw_affiliation_strings":["Computer Science Department, University of Minnesota, 55455, Minneapolis, MN, USA","Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Minnesota, 55455, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052495839","display_name":"Biao Gao","orcid":"https://orcid.org/0000-0003-0914-7888"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Biao Gao","raw_affiliation_strings":["Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005013807","display_name":"Ronald Graham","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald L. Graham","raw_affiliation_strings":["AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057316735","display_name":"Zi-Cheng Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zi-Cheng Liu","raw_affiliation_strings":["Computer Science Department, Princeton University, 08544, Princeton, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Princeton University, 08544, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036031118","display_name":"Peng\u2010Jun Wan","orcid":"https://orcid.org/0000-0001-7926-5711"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng-Jun Wan","raw_affiliation_strings":["Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.3801,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.87109064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"4","first_page":"351","last_page":"370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9847999811172485,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9531000256538391,"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.9093873500823975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8452712297439575},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8151799440383911},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5933150053024292},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5485799908638},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.5138106942176819},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4650728702545166},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45576342940330505},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4341370165348053},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.43008214235305786},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3707854747772217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11636605858802795},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11614489555358887},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06210097670555115}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.9093873500823975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8452712297439575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8151799440383911},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5933150053024292},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5485799908638},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.5138106942176819},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4650728702545166},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45576342940330505},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4341370165348053},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.43008214235305786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3707854747772217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11636605858802795},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11614489555358887},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06210097670555115},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02189328","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02189328","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02189328.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 &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.8918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.8918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iit.edu/~wan/Journal/dcg93.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/bf02189328","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02189328","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02189328.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 &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2062191077.pdf","grobid_xml":"https://content.openalex.org/works/W2062191077.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1972390207","https://openalex.org/W1987050938","https://openalex.org/W1992565319","https://openalex.org/W2017318533","https://openalex.org/W2018943178","https://openalex.org/W2020112047","https://openalex.org/W2024833542","https://openalex.org/W2041586232","https://openalex.org/W2049325932","https://openalex.org/W2060380213","https://openalex.org/W2069712919","https://openalex.org/W2086709935","https://openalex.org/W2091673977","https://openalex.org/W2139311061","https://openalex.org/W6600911440"],"related_works":["https://openalex.org/W2090953203","https://openalex.org/W3194189065","https://openalex.org/W3094179009","https://openalex.org/W2056824842","https://openalex.org/W2294873576","https://openalex.org/W4289864840","https://openalex.org/W4299959263","https://openalex.org/W3017048616","https://openalex.org/W2963314455","https://openalex.org/W2012030066"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
