{"id":"https://openalex.org/W4403792280","doi":"https://doi.org/10.1007/s00453-024-01278-5","title":"Better Hardness Results for the Minimum Spanning Tree Congestion Problem","display_name":"Better Hardness Results for the Minimum Spanning Tree Congestion Problem","publication_year":2024,"publication_date":"2024-10-26","ids":{"openalex":"https://openalex.org/W4403792280","doi":"https://doi.org/10.1007/s00453-024-01278-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-024-01278-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01278-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01278-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","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/s00453-024-01278-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002642353","display_name":"Huong Luu","orcid":"https://orcid.org/0009-0003-4696-4673"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Huong Luu","raw_affiliation_strings":["University of California at Riverside, Riverside, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Riverside, Riverside, USA","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024529572","display_name":"Marek Chrob\u00e1k","orcid":"https://orcid.org/0000-0002-8673-2709"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marek Chrobak","raw_affiliation_strings":["University of California at Riverside, Riverside, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Riverside, Riverside, USA","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002642353"],"corresponding_institution_ids":["https://openalex.org/I103635307"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23028077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"1","first_page":"148","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T12288","display_name":"Optimization and Search Problems","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.6187918782234192},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5612967610359192},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5180333256721497},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5133151412010193},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.4934936761856079},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45097726583480835},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.44722500443458557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4313249886035919},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24354612827301025}],"concepts":[{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.6187918782234192},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5612967610359192},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5180333256721497},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5133151412010193},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.4934936761856079},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45097726583480835},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.44722500443458557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4313249886035919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24354612827301025}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-024-01278-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01278-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01278-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00453-024-01278-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01278-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01278-5.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4300000071525574,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403792280.pdf","grobid_xml":"https://content.openalex.org/works/W4403792280.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1489598663","https://openalex.org/W1512588309","https://openalex.org/W1565801653","https://openalex.org/W1595216699","https://openalex.org/W1968079464","https://openalex.org/W1980466385","https://openalex.org/W1985209733","https://openalex.org/W2008906655","https://openalex.org/W2012899511","https://openalex.org/W2019040312","https://openalex.org/W2046337003","https://openalex.org/W2051540665","https://openalex.org/W2056879109","https://openalex.org/W2081820323","https://openalex.org/W2129575457","https://openalex.org/W2150917267","https://openalex.org/W2152986618","https://openalex.org/W2153573559","https://openalex.org/W2599142459","https://openalex.org/W2912257407","https://openalex.org/W3020636320","https://openalex.org/W4210631930","https://openalex.org/W4296553954","https://openalex.org/W4324009412"],"related_works":["https://openalex.org/W2099915933","https://openalex.org/W2418231958","https://openalex.org/W4380840098","https://openalex.org/W3116169590","https://openalex.org/W2044443696","https://openalex.org/W1703428550","https://openalex.org/W2503538928","https://openalex.org/W3101281637","https://openalex.org/W2390742649","https://openalex.org/W1561849181"],"abstract_inverted_index":{"Abstract":[0],"In":[1,101],"the":[2,13,31,40,48,88,102,185,192,214,250,294,308,312],"spanning":[3,19,130],"tree":[4,20,131],"congestion":[5,32,133,322],"problem,":[6,107],"given":[7],"a":[8,18,129,179],"connected":[9],"graph":[10],"G":[11,23,45,127],",":[12,121,175],"objective":[14],"is":[15,39,61,77,83,139,154,269,323],"to":[16,63,124,315,348],"compute":[17],"T":[21,38,52],"in":[22,44,51,210],"that":[24,141,256,320],"minimizes":[25],"its":[26,75],"maximum":[27],"edge":[28,35],"congestion,":[29],"where":[30],"of":[33,37,42,105,182,188,217,328,350],"an":[34,244],"e":[36,57],"number":[41],"edges":[43],"for":[46,164,220,279,326],"which":[47],"unique":[49],"path":[50],"between":[53],"their":[54],"endpoints":[55],"traverses":[56],".":[58,137,290],"The":[59],"problem":[60,219],"known":[62,86,140],"be":[64,92,208],"$$\\mathbb{N}\\mathbb{P}$$":[65,155,270],"<mml:math":[66,111,144,156,167,197,227,259,271,282,297,337],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[67,112,145,157,168,198,228,260,272,283,298,338],"<mml:mrow>":[68,113,114,146,147,158,169,199,200,229,261,262,273,284,299,339,340],"<mml:mi>N</mml:mi>":[69,159,274],"<mml:mi>P</mml:mi>":[70,160,275],"</mml:mrow>":[71,116,119,149,152,161,173,202,205,241,264,267,276,288,303,342,345],"</mml:math>":[72,120,153,162,174,206,242,268,277,289,304,346],"-hard,":[73],"but":[74],"approximability":[76],"still":[78],"poorly":[79],"understood,":[80],"and":[81,176,306,353],"it":[82],"not":[84],"even":[85,325],"whether":[87],"optimum":[89],"solution":[90],"can":[91,207],"efficiently":[93],"approximated":[94],"with":[95,132,213],"ratio":[96,187,314],"o":[97],"(":[98],"n":[99],").":[100],"decision":[103],"version":[104],"this":[106,177,218],"denoted":[108],"$${\\varvec{K}-\\textsf":[109,142,257,335],"{STC}}$$":[110,143,196,258,336],"<mml:mi>K</mml:mi>":[115,148,170,230,263,285,300,341],"<mml:mo>-</mml:mo>":[117,150,203,265,343],"<mml:mi>STC</mml:mi>":[118,151,204,266,344],"we":[122,332,354],"need":[123],"determine":[125],"if":[126],"has":[128],"at":[134],"most":[135],"K":[136],"It":[138],"-complete":[163,278],"$$K\\ge":[165,280],"8$$":[166],"<mml:mo>\u2265</mml:mo>":[171,286],"<mml:mn>8</mml:mn>":[172],"implies":[178],"lower":[180,309],"bound":[181,310],"1.125":[183],"on":[184,311],"approximation":[186,313],"minimizing":[189,321],"congestion.":[190],"On":[191],"other":[193],"hand,":[194],"$${\\varvec{3}-\\textsf":[195],"<mml:mn>3</mml:mn>":[201],"solved":[209],"polynomial":[211],"time,":[212],"complexity":[215],"status":[216],"$$K\\in":[221],"{":[222],"\\left\\{":[223],"4,5,6,7":[224],"\\right\\}":[225],"}$$":[226],"<mml:mo>\u2208</mml:mo>":[231],"<mml:mfenced>":[232],"<mml:mn>4</mml:mn>":[233,302],"<mml:mo>,</mml:mo>":[234,236,238],"<mml:mn>5</mml:mn>":[235,287],"<mml:mn>6</mml:mn>":[237],"<mml:mn>7</mml:mn>":[239],"</mml:mfenced>":[240],"remaining":[243],"open":[245],"problem.":[246],"We":[247],"substantially":[248],"improve":[249],"earlier":[251],"hardness":[252],"results":[253],"by":[254,318],"proving":[255],"5$$":[281],"This":[291],"leaves":[292],"only":[293],"case":[295],"$$K=4$$":[296],"<mml:mo>=</mml:mo>":[301],"open,":[305],"improves":[307],"1.2.":[316],"Motivated":[317],"evidence":[319],"hard":[324],"graphs":[327,349],"small":[329],"constant":[330],"radius,":[331],"also":[333],"consider":[334],"restricted":[347],"radius":[351],"2,":[352]},"counts_by_year":[],"updated_date":"2026-03-09T07:00:12.390032","created_date":"2025-10-10T00:00:00"}