{"id":"https://openalex.org/W2053792000","doi":"https://doi.org/10.1137/s1052623494275069","title":"A Dynamic Adaptive Relaxation Scheme Applied to the Euclidean Steiner Minimal Tree Problem","display_name":"A Dynamic Adaptive Relaxation Scheme Applied to the Euclidean Steiner Minimal Tree Problem","publication_year":1997,"publication_date":"1997-11-01","ids":{"openalex":"https://openalex.org/W2053792000","doi":"https://doi.org/10.1137/s1052623494275069","mag":"2053792000"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623494275069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494275069","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5011909165","display_name":"Fran\u00e7ois Chapeau\u2010Blondeau","orcid":"https://orcid.org/0000-0003-0536-7146"},"institutions":[{"id":"https://openalex.org/I49451733","display_name":"Universit\u00e9 d'Angers","ror":"https://ror.org/04yrqp957","country_code":"FR","type":"education","lineage":["https://openalex.org/I49451733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Chapeau-Blondeau","raw_affiliation_strings":["Facult\u00e9 des Sciences, Universit\u00e9 d'Angers, 2 boulevard Lavoisier, 49000 Angers, France"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 des Sciences, Universit\u00e9 d'Angers, 2 boulevard Lavoisier, 49000 Angers, France","institution_ids":["https://openalex.org/I49451733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060995071","display_name":"Fabrice Janez","orcid":null},"institutions":[{"id":"https://openalex.org/I49451733","display_name":"Universit\u00e9 d'Angers","ror":"https://ror.org/04yrqp957","country_code":"FR","type":"education","lineage":["https://openalex.org/I49451733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fabrice Janez","raw_affiliation_strings":["Laboratoire d'Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, Universit\u00e9 d'Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, Universit\u00e9 d'Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France","institution_ids":["https://openalex.org/I49451733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110660367","display_name":"Jean-Louis Ferrier","orcid":null},"institutions":[{"id":"https://openalex.org/I49451733","display_name":"Universit\u00e9 d'Angers","ror":"https://ror.org/04yrqp957","country_code":"FR","type":"education","lineage":["https://openalex.org/I49451733"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Louis Ferrier","raw_affiliation_strings":["Laboratoire d'Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, Universit\u00e9 d'Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, Universit\u00e9 d'Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France","institution_ids":["https://openalex.org/I49451733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110660367"],"corresponding_institution_ids":["https://openalex.org/I49451733"],"apc_list":null,"apc_paid":null,"fwci":1.0786,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.77335081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"4","first_page":"1037","last_page":"1053"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9894999861717224,"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":0.9894999861717224,"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/T12161","display_name":"Plant Surface Properties and Treatments","score":0.9193000197410583,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9017999768257141,"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":0.9406286478042603},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7975133657455444},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.721747636795044},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.6169389486312866},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.559027910232544},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.48051366209983826},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.47705236077308655},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4606499671936035},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4544752240180969},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39054393768310547},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.14615431427955627},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11563435196876526}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.9406286478042603},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7975133657455444},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.721747636795044},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.6169389486312866},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.559027910232544},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.48051366209983826},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.47705236077308655},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4606499671936035},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4544752240180969},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39054393768310547},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.14615431427955627},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11563435196876526},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1052623494275069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494275069","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.520.8649","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.520.8649","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://perso-laris.univ-angers.fr/~chapeau/papers/siam1997.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00843948v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00843948","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 1997, 7 (4), pp.1037-1053","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W55191700","https://openalex.org/W284492748","https://openalex.org/W293887236","https://openalex.org/W1567794274","https://openalex.org/W1597286183","https://openalex.org/W1971779258","https://openalex.org/W1975807353","https://openalex.org/W1990488643","https://openalex.org/W1993251782","https://openalex.org/W2002245835","https://openalex.org/W2007169240","https://openalex.org/W2007610503","https://openalex.org/W2011065039","https://openalex.org/W2017318533","https://openalex.org/W2019357066","https://openalex.org/W2022150791","https://openalex.org/W2024060531","https://openalex.org/W2024633374","https://openalex.org/W2025638429","https://openalex.org/W2029791926","https://openalex.org/W2034874993","https://openalex.org/W2041858001","https://openalex.org/W2042477130","https://openalex.org/W2042492403","https://openalex.org/W2044176843","https://openalex.org/W2045286914","https://openalex.org/W2047422346","https://openalex.org/W2051682049","https://openalex.org/W2051719061","https://openalex.org/W2060380213","https://openalex.org/W2061614302","https://openalex.org/W2061712794","https://openalex.org/W2064791171","https://openalex.org/W2067651881","https://openalex.org/W2070582626","https://openalex.org/W2076569589","https://openalex.org/W2085655777","https://openalex.org/W2086709935","https://openalex.org/W2088967712","https://openalex.org/W2092104934","https://openalex.org/W2096527938","https://openalex.org/W2102308073","https://openalex.org/W2116935655","https://openalex.org/W2156503228","https://openalex.org/W2157274506","https://openalex.org/W2479645628","https://openalex.org/W2749671165"],"related_works":["https://openalex.org/W1561849181","https://openalex.org/W3187208706","https://openalex.org/W3081212354","https://openalex.org/W98489388","https://openalex.org/W3116169590","https://openalex.org/W1985149601","https://openalex.org/W3101281637","https://openalex.org/W1703428550","https://openalex.org/W1964611452","https://openalex.org/W2390742649"],"abstract_inverted_index":{"The":[0],"Steiner":[1,87,136,166,203,230],"problem":[2,7,184,204],"is":[3,54,80,142,170],"an":[4,68,76,119,224],"NP-hard":[5],"optimization":[6],"which":[8,62,110],"consists":[9],"of":[10,18,27,93,106,148,156,178,194,198,201,213,232],"finding":[11],"the":[12,22,57,104,132,135,146,149,165,179,195,199,202,214,220,228],"minimal-length":[13],"tree":[14,60,88,231],"connecting":[15],"a":[16,84,90,100,107,154,157,206,209],"set":[17],"N":[19,47],"points":[20],"in":[21,33,67,118,153],"Euclidean":[23],"plane.":[24],"Exact":[25],"methods":[26],"resolution":[28],"currently":[29],"available":[30,181],"are":[31],"exponential":[32],"N,":[34],"making":[35],"exact":[36],"minimal":[37,229],"trees":[38],"accessible":[39],"for":[40,164,227,238],"only":[41],"small":[42],"size":[43],"problems":[44],"(up":[45],"to":[46,82,134,144,172,187,208],"\\approx":[48],"100).":[49],"An":[50],"acceptable":[51],"suboptimal":[52],"solution":[53,133,200],"provided":[55],"by":[56],"minimum":[58,92],"spanning":[59],"(MST)":[61],"has":[63],"been":[64],"shown":[65,171],"computable":[66],"O(N":[69,160],"log":[70,161],"N)":[71,162],"step.":[72],"We":[73],"propose":[74],"here":[75],"O(N)":[77,139],"process":[78],"that":[79,177],"able":[81],"relax":[83],"given":[85],"initial":[86],"into":[89],"local":[91,128],"its":[94,123],"length.":[95],"This":[96,151],"process,":[97],"based":[98],"on":[99],"physical":[101],"analogy,":[102],"simulates":[103],"dynamics":[105],"fluid":[108],"film":[109],"relaxes":[111],"under":[112],"surface":[113],"tension":[114],"forces":[115],"and":[116,222],"stabilizes":[117],"equilibrium":[120],"configuration":[121],"minimizing":[122],"total":[124],"length,":[125],"through":[126],"purely":[127],"interactions.":[129],"To":[130],"improve":[131],"problem,":[137,167],"this":[138],"relaxation":[140],"scheme":[141],"applied":[143],"reduce":[145],"length":[147,216,226],"MST.":[150],"results":[152],"heuristic":[155],"very":[158],"low":[159],"complexity":[163],"whose":[168],"performance":[169],"compare":[173],"quite":[174],"favorably":[175],"with":[176],"best":[180],"heuristics.":[182],"Large":[183],"sizes":[185],"up":[186],"N=10000":[188],"were":[189],"successfully":[190],"tackled.":[191],"A":[192],"characterization":[193],"asymptotic":[196],"behavior":[197],"shows":[205],"stabilization":[207],"nonvanishing":[210],"positive":[211],"value":[212],"average":[215,225],"reduction":[217],"achieved":[218],"over":[219],"MST":[221],"predicts":[223],"about":[233],"3%":[234],"below":[235],"0.65":[236],"N1/2":[237],"large":[239],"N.":[240]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
