{"id":"https://openalex.org/W7131371754","doi":"https://doi.org/10.48550/arxiv.2602.19879","title":"The Bidirected Cut Relaxation for Steiner Tree: Better Integrality Gap Bounds and the Limits of Moat Growing","display_name":"The Bidirected Cut Relaxation for Steiner Tree: Better Integrality Gap Bounds and the Limits of Moat Growing","publication_year":2026,"publication_date":"2026-02-23","ids":{"openalex":"https://openalex.org/W7131371754","doi":"https://doi.org/10.48550/arxiv.2602.19879"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.19879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.19879","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114634060","display_name":"Paul Paschmanns","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paschmanns, Paul","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065421870","display_name":"Vera Traub","orcid":"https://orcid.org/0000-0001-9749-2600"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Traub, Vera","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.7330999970436096,"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":0.7330999970436096,"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":0.19089999794960022,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.030300000682473183,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.7717000246047974},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.7368000149726868},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6003000140190125},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5600000023841858},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5514000058174133},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.477400004863739},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.42669999599456787}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8112999796867371},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.7717000246047974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7584999799728394},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.7368000149726868},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6003000140190125},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5600000023841858},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5318999886512756},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.19879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.19879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.19879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Steiner":[1,30,120],"Tree":[2,31],"problem":[3],"asks":[4],"for":[5,29],"the":[6,15,23,33,39,53,77,89,101,107,125,138,147,153,193],"cheapest":[7],"way":[8],"of":[9,14,22,42,80,92,104,137,150,166],"connecting":[10],"a":[11,46,112,134,163],"given":[12],"subset":[13],"vertices":[16],"in":[17],"an":[18,118,181,189],"undirected":[19],"graph.":[20],"One":[21],"most":[24,96,130],"prominent":[25],"linear":[26],"programming":[27],"relaxations":[28],"is":[32,45,61,82,94,117,128],"Bidirected":[34],"Cut":[35],"Relaxation":[36],"(BCR).":[37],"Determining":[38],"integrality":[40,78,90,126,154,182],"gap":[41,79,91,127,183],"this":[43],"relaxation":[44],"long-standing":[47],"open":[48],"question.":[49],"For":[50,106],"several":[51],"decades,":[52],"best":[54],"known":[55],"upper":[56],"bound":[57,103,149],"was":[58],"2,":[59],"which":[60],"achievable":[62],"by":[63,132,141],"standard":[64],"techniques.":[65],"Only":[66],"very":[67],"recently,":[68],"Byrka,":[69],"Grandoni,":[70],"and":[71],"Traub":[72],"[FOCS":[73],"2024]":[74],"showed":[75],"that":[76,88,124,172],"BCR":[81,93],"strictly":[83],"below":[84,184],"2.":[85],"We":[86],"prove":[87,171],"at":[95,129],"1.898,":[97],"improving":[98],"significantly":[99],"on":[100,152],"previous":[102],"1.9988.":[105],"important":[108],"special":[109],"case":[110],"where":[111],"terminal":[113],"minimum":[114],"spanning":[115],"tree":[116],"optimal":[119],"tree,":[121],"we":[122,156,170,187],"show":[123],"12/7,":[131],"providing":[133],"tight":[135],"analysis":[136],"dual-growth":[139],"procedure":[140,161],"Byrka":[142],"et":[143],"al.":[144],"To":[145],"obtain":[146],"general":[148],"1.898":[151],"gap,":[155],"generalize":[157],"their":[158],"dual":[159,178],"growth":[160],"to":[162,192],"broad":[164],"class":[165],"moat-growing":[167,175],"algorithms.":[168],"Moreover,":[169],"no":[173],"such":[174],"algorithm":[176],"yields":[177],"solutions":[179],"certifying":[180],"12/7.":[185],"Finally,":[186],"observe":[188],"interesting":[190],"connection":[191],"Hypergraphic":[194],"Relaxation.":[195]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-26T00:00:00"}
