{"id":"https://openalex.org/W2149509209","doi":"https://doi.org/10.1002/net.3230260411","title":"An O(N<sup>2</sup>) heuristic for steiner minimal trees in E<sup>3</sup>","display_name":"An O(N<sup>2</sup>) heuristic for steiner minimal trees in E<sup>3</sup>","publication_year":1995,"publication_date":"1995-12-01","ids":{"openalex":"https://openalex.org/W2149509209","doi":"https://doi.org/10.1002/net.3230260411","mag":"2149509209"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230260411","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230260411","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5101974532","display_name":"J. MacGregor Smith","orcid":"https://orcid.org/0000-0002-6147-5806"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. MacGregor Smith","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, Massachusetts 01003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, Massachusetts 01003","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049903422","display_name":"R. Weiss","orcid":null},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rich Weiss","raw_affiliation_strings":["Department of Computer and Information Systems, University of Massachusetts, Amherst, Massachusetts 01003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Systems, University of Massachusetts, Amherst, Massachusetts 01003","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052359058","display_name":"Minoo Patel","orcid":"https://orcid.org/0000-0002-8562-495X"},"institutions":[{"id":"https://openalex.org/I1334696734","display_name":"American Airlines (United States)","ror":"https://ror.org/05jh79p16","country_code":"US","type":"company","lineage":["https://openalex.org/I1334696734"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Minoo Patel","raw_affiliation_strings":["United Airlines Executive Offices, EXOEB, P.O. Box 66100, Chicago, Illinois 60666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"United Airlines Executive Offices, EXOEB, P.O. Box 66100, Chicago, Illinois 60666","institution_ids":["https://openalex.org/I1334696734"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.3736,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.65176322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"4","first_page":"273","last_page":"289"},"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/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9879000186920166,"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":0.777238130569458},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7470128536224365},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.7130981087684631},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6692216992378235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46838265657424927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4619939625263214},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4609980583190918},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4209875166416168},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3646218180656433},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.298223078250885},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06616434454917908}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.777238130569458},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7470128536224365},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.7130981087684631},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6692216992378235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46838265657424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4619939625263214},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4609980583190918},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4209875166416168},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3646218180656433},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.298223078250885},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06616434454917908}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230260411","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230260411","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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":38,"referenced_works":["https://openalex.org/W81711424","https://openalex.org/W382230777","https://openalex.org/W1528622396","https://openalex.org/W1603536826","https://openalex.org/W1659568777","https://openalex.org/W1976925751","https://openalex.org/W1980404739","https://openalex.org/W1985019992","https://openalex.org/W1990488643","https://openalex.org/W1992843866","https://openalex.org/W2011039300","https://openalex.org/W2011065039","https://openalex.org/W2012130001","https://openalex.org/W2017927472","https://openalex.org/W2022150791","https://openalex.org/W2024833542","https://openalex.org/W2025638429","https://openalex.org/W2031746936","https://openalex.org/W2042477130","https://openalex.org/W2042492403","https://openalex.org/W2049010908","https://openalex.org/W2060380213","https://openalex.org/W2064791171","https://openalex.org/W2067651881","https://openalex.org/W2073692857","https://openalex.org/W2085655777","https://openalex.org/W2086709935","https://openalex.org/W2088967712","https://openalex.org/W2094055387","https://openalex.org/W2128865241","https://openalex.org/W2172222998","https://openalex.org/W3148632216","https://openalex.org/W4237579241","https://openalex.org/W4238196893","https://openalex.org/W4243812205","https://openalex.org/W4252925418","https://openalex.org/W4292081294","https://openalex.org/W6603333602"],"related_works":["https://openalex.org/W2359979928","https://openalex.org/W2161182859","https://openalex.org/W2368353614","https://openalex.org/W2118320476","https://openalex.org/W2390369954","https://openalex.org/W1529719486","https://openalex.org/W4232052003","https://openalex.org/W2373917503","https://openalex.org/W1503036335","https://openalex.org/W2021517364"],"abstract_inverted_index":{"Abstract":[0],"Even":[1],"though":[2],"the":[3,12,36,48,54,57],"problem":[4,37,55],"of":[5,50],"computing":[6],"Steiner":[7],"minimal":[8],"trees":[9],"(SMTs)":[10],"in":[11,27,38,60],"plane":[13],"is":[14,41],"well":[15],"known":[16],"to":[17,62],"be":[18],"NP":[19],"\u2010hard,":[20],"There":[21],"exist":[22],"heuristic":[23,52],"algorithms":[24],"which":[25],"run":[26],"polynomial":[28],"time.":[29],"Recent":[30],"research":[31],"results":[32,67],"have":[33],"shown":[34],"that":[35],"three":[39],"dimensions":[40],"demonstrably":[42],"more":[43],"difficult.":[44],"This":[45],"paper":[46],"approaches":[47],"development":[49],"a":[51],"for":[53],"utilizing":[56],"Delaunay":[58],"triangulation":[59],"3\u2010space":[61],"compute":[63],"suboptimal":[64],"SMTs.":[65],"Computational":[66],"are":[68],"also":[69],"provided.":[70]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
