{"id":"https://openalex.org/W2085242823","doi":"https://doi.org/10.1007/bf02187919","title":"A decomposition theorem on Euclidean Steiner minimal trees","display_name":"A decomposition theorem on Euclidean Steiner minimal trees","publication_year":1988,"publication_date":"1988-12-01","ids":{"openalex":"https://openalex.org/W2085242823","doi":"https://doi.org/10.1007/bf02187919","mag":"2085242823"},"language":"en","primary_location":{"id":"doi:10.1007/bf02187919","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187919","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187919.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 & 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/BF02187919.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065344888","display_name":"F. K. Hwang","orcid":"https://orcid.org/0000-0003-3913-0198"},"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"]},{"id":"https://openalex.org/I72090969","display_name":"Nokia (United States)","ror":"https://ror.org/038km2573","country_code":"US","type":"company","lineage":["https://openalex.org/I2738502077","https://openalex.org/I72090969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F. K. Hwang","raw_affiliation_strings":["AT&T Bell Laboratories, Murray Hill, New Jersey, USA","AT&T BELL LABORATORIES, Murray Hill, USA"],"affiliations":[{"raw_affiliation_string":"AT&T Bell Laboratories, Murray Hill, New Jersey, USA","institution_ids":["https://openalex.org/I1283103587"]},{"raw_affiliation_string":"AT&T BELL LABORATORIES, Murray Hill, USA","institution_ids":["https://openalex.org/I72090969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101491147","display_name":"Ge Song","orcid":"https://orcid.org/0000-0002-2569-8105"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. D. Song","raw_affiliation_strings":["Quiquihaer Light Engineering College, Heilungjiang, China","Quiquihaer Light Engineering College, Heilungjiang, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Quiquihaer Light Engineering College, Heilungjiang, China","institution_ids":[]},{"raw_affiliation_string":"Quiquihaer Light Engineering College, Heilungjiang, China#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026028312","display_name":"G. Y. Ting","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Y. Ting","raw_affiliation_strings":["Quiquihaer Teacher's College, Heilungjiang, China","Quiquihaer Teacher's College, Heilungjiang, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Quiquihaer Teacher's College, Heilungjiang, China","institution_ids":[]},{"raw_affiliation_string":"Quiquihaer Teacher's College, Heilungjiang, China#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037860988","display_name":"Ding\u2010Zhu Du","orcid":"https://orcid.org/0000-0002-7345-2185"},"institutions":[{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]},{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Z. Du","raw_affiliation_strings":["Mathematics Science Research Institute, Berkeley, California, USA","Mathematics Science Research Institute, Berkeley, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematics Science Research Institute, Berkeley, California, USA","institution_ids":["https://openalex.org/I1297971548"]},{"raw_affiliation_string":"Mathematics Science Research Institute, Berkeley, USA#TAB#","institution_ids":["https://openalex.org/I73544541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065344888"],"corresponding_institution_ids":["https://openalex.org/I1283103587","https://openalex.org/I72090969"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.1025,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.87068615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"4","first_page":"367","last_page":"382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9965999722480774,"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/T10142","display_name":"Formal Methods in Verification","score":0.9922999739646912,"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":0.906988263130188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8673344850540161},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.73176109790802},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6673977375030518},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6115996837615967},{"id":"https://openalex.org/keywords/decomposition-theorem","display_name":"Decomposition theorem","score":0.6058652997016907},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4521579146385193},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45027559995651245},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.44818711280822754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06981539726257324},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06349310278892517}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.906988263130188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8673344850540161},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.73176109790802},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6673977375030518},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6115996837615967},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.6058652997016907},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4521579146385193},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45027559995651245},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44818711280822754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06981539726257324},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06349310278892517},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02187919","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187919","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187919.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 & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/bf02187919","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187919","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187919.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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2085242823.pdf","grobid_xml":"https://content.openalex.org/works/W2085242823.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2060380213","https://openalex.org/W2086709935","https://openalex.org/W2090953203","https://openalex.org/W2094076885","https://openalex.org/W2156503228"],"related_works":["https://openalex.org/W2161182859","https://openalex.org/W2118320476","https://openalex.org/W1503036335","https://openalex.org/W2025658531","https://openalex.org/W2011703460","https://openalex.org/W1992380975","https://openalex.org/W2080581853","https://openalex.org/W3201893458","https://openalex.org/W2206601122","https://openalex.org/W2085242823"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}