{"id":"https://openalex.org/W4308933888","doi":"https://doi.org/10.1007/s11590-022-01949-8","title":"Polyhedral results and stronger Lagrangean bounds for stable spanning trees","display_name":"Polyhedral results and stronger Lagrangean bounds for stable spanning trees","publication_year":2022,"publication_date":"2022-11-11","ids":{"openalex":"https://openalex.org/W4308933888","doi":"https://doi.org/10.1007/s11590-022-01949-8"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-022-01949-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01949-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01949-8.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01949-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062994676","display_name":"Phillippe Samer","orcid":"https://orcid.org/0000-0001-9007-0237"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Phillippe Samer","raw_affiliation_strings":["Department of Informatics, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway"],"raw_orcid":"https://orcid.org/0000-0001-9007-0237","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016839320","display_name":"Dag Haugland","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Dag Haugland","raw_affiliation_strings":["Department of Informatics, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway"],"raw_orcid":"https://orcid.org/0000-0003-1110-3382","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062994676"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.2056,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7803781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"17","issue":"6","first_page":"1317","last_page":"1335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5788825154304504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4276793897151947},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3913412094116211}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5788825154304504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4276793897151947},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3913412094116211}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-022-01949-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01949-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01949-8.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11590-022-01949-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01949-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01949-8.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3538256737","display_name":null,"funder_award_id":"249994","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"},{"id":"https://openalex.org/G5906860864","display_name":null,"funder_award_id":"249994 CLASSIS","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308933888.pdf","grobid_xml":"https://content.openalex.org/works/W4308933888.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W179052057","https://openalex.org/W1481577095","https://openalex.org/W1982713256","https://openalex.org/W1984804966","https://openalex.org/W1989023497","https://openalex.org/W1991528957","https://openalex.org/W2002792327","https://openalex.org/W2013850148","https://openalex.org/W2031244688","https://openalex.org/W2046709864","https://openalex.org/W2050014122","https://openalex.org/W2051450977","https://openalex.org/W2069618627","https://openalex.org/W2077278144","https://openalex.org/W2090246427","https://openalex.org/W2116638623","https://openalex.org/W2131987076","https://openalex.org/W2159446692","https://openalex.org/W2160429376","https://openalex.org/W2165012734","https://openalex.org/W2505968561","https://openalex.org/W2611825068","https://openalex.org/W2806852865","https://openalex.org/W2913987580","https://openalex.org/W2916470116","https://openalex.org/W2963351303","https://openalex.org/W3104695357","https://openalex.org/W3105285671","https://openalex.org/W3109104928","https://openalex.org/W3127315540","https://openalex.org/W4256046638","https://openalex.org/W6929602941","https://openalex.org/W7111281088"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,18,31,38,44,133,177,228,253,301],"graph":[3,147],"$$G=(V,E)$$":[4],"<mml:math":[5,60,86,95,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[6,61,87,96,151],"<mml:mrow>":[7,62,152],"<mml:mi>G</mml:mi>":[8],"<mml:mo>=</mml:mo>":[9,154],"<mml:mo>(</mml:mo>":[10,155],"<mml:mi>V</mml:mi>":[11],"<mml:mo>,</mml:mo>":[12,68,157],"<mml:mi>E</mml:mi>":[13,156],"<mml:mo>)</mml:mo>":[14,159],"</mml:mrow>":[15,76,160],"</mml:math>":[16,77,92,101,161],"and":[17,93,171,189],"set":[19,39,194],"C":[20],"of":[21,24,40,82,116,136,167,187,196,215,230,239,275,281,294],"unordered":[22],"pairs":[23],"edges":[25,41,84],"regarded":[26],"as":[27],"being":[28],"in":[29,35,47,103,143,176,198,217,278,290,300],"conflict,":[30],"stable":[32,120,141,193],"spanning":[33,45,121,184],"tree":[34,46,185],"G":[36,48,188],"is":[37,102,123,202,226,272,297],"T":[42,104],"inducing":[43],",":[49,78],"such":[50],"that":[51,256],"for":[52,232],"each":[53],"$$\\left\\{":[54],"e_i,":[55],"e_j":[56],"\\right\\}":[57],"\\in":[58],"C$$":[59],"<mml:mfenced>":[63],"<mml:msub>":[64,69,88,97],"<mml:mi>e</mml:mi>":[65,70,89,98],"<mml:mi>i</mml:mi>":[66,90],"</mml:msub>":[67,72,91,100],"<mml:mi>j</mml:mi>":[71,99],"</mml:mfenced>":[73],"<mml:mo>\u2208</mml:mo>":[74],"<mml:mi>C</mml:mi>":[75,158],"at":[79],"most":[80],"one":[81],"the":[83,113,128,144,168,183,190,199,213,218,237,258,270,276,288,295],"$$e_i$$":[85],"$$e_j$$":[94],".":[105,162],"The":[106],"existing":[107],"work":[108],"on":[109],"Lagrangean":[110,178,234,266],"algorithms":[111],"to":[112,125,204,221],"-hard":[114],"problem":[115,220],"finding":[117],"minimum":[118],"weight":[119],"trees":[122],"limited":[124],"relaxations":[126],"with":[127,236,262],"integrality":[129],"property.":[130],"We":[131,163,247],"exploit":[132],"new":[134],"relaxation":[135,235],"this":[137],"problem:":[138],"fixed":[139,191],"cardinality":[140,192],"sets":[142],"underlying":[145],"conflict":[146],"$$H":[148],"=(E,C)$$":[149],"<mml:mi>H</mml:mi>":[153],"find":[164],"interesting":[165],"properties":[166],"corresponding":[169],"polytope,":[170],"determine":[172],"stronger":[173],"dual":[174,219,254],"bounds":[175],"decomposition":[179],"framework,":[180],"optimizing":[181],"over":[182,243],"polytope":[186,195],"H":[197],"subproblems.":[200,246],"This":[201],"equivalent":[203],"dualizing":[205],"exponentially":[206],"many":[207],"subtour":[208],"elimination":[209],"constraints,":[210],"while":[211],"limiting":[212],"number":[214],"multipliers":[216,263],"|":[222],"E":[223],"|.":[224],"It":[225],"also":[227],"proof":[229],"concept":[231],"combining":[233],"power":[238],"integer":[240],"programming":[241],"solvers":[242],"strongly":[244],"NP-hard":[245],"present":[248],"encouraging":[249],"computational":[250],"results":[251],"using":[252],"method":[255],"comprises":[257],"Volume":[259],"Algorithm,":[260],"initialized":[261],"determined":[264],"by":[265],"dual-ascent.":[267],"In":[268],"particular,":[269],"bound":[271],"within":[273],"5.5%":[274],"optimum":[277,289],"146":[279],"out":[280],"200":[282],"benchmark":[283],"instances;":[284],"it":[285],"actually":[286],"matches":[287],"75":[291],"cases.":[292],"All":[293],"implementation":[296],"made":[298],"available":[299],"free,":[302],"open-source":[303],"repository.":[304]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
