{"id":"https://openalex.org/W4415090694","doi":"https://doi.org/10.48550/arxiv.2509.10626","title":"Optimal Multimarginal Schr\u00f6dinger Bridge: Minimum Spanning Tree over Measure-valued Vertices","display_name":"Optimal Multimarginal Schr\u00f6dinger Bridge: Minimum Spanning Tree over Measure-valued Vertices","publication_year":2025,"publication_date":"2025-09-12","ids":{"openalex":"https://openalex.org/W4415090694","doi":"https://doi.org/10.48550/arxiv.2509.10626"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.10626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.10626","pdf_url":"https://arxiv.org/pdf/2509.10626","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.10626","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093013953","display_name":"Georgiy A. Bondar","orcid":"https://orcid.org/0009-0008-1369-2495"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bondar, Georgiy A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029714029","display_name":"Abhishek Halder","orcid":"https://orcid.org/0000-0002-1509-5853"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Halder, Abhishek","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/T10320","display_name":"Neural Networks and Applications","score":0.9265000224113464,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9265000224113464,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11476","display_name":"Graph theory and applications","score":0.909600019454956,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.7817999720573425},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.6912000179290771},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.5593000054359436},{"id":"https://openalex.org/keywords/k-minimum-spanning-tree","display_name":"k-minimum spanning tree","score":0.4846999943256378},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47850000858306885},{"id":"https://openalex.org/keywords/minimum-cut","display_name":"Minimum cut","score":0.47690001130104065},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.4510999917984009},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.40230000019073486}],"concepts":[{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.7817999720573425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577000260353088},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.6912000179290771},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6710000038146973},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.5593000054359436},{"id":"https://openalex.org/C202750272","wikidata":"https://www.wikidata.org/wiki/Q6322849","display_name":"k-minimum spanning tree","level":5,"score":0.4846999943256378},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47850000858306885},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.4510999917984009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45080000162124634},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.37950000166893005},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.34700000286102295},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.33550000190734863},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.335099995136261},{"id":"https://openalex.org/C23394520","wikidata":"https://www.wikidata.org/wiki/Q4919350","display_name":"Shortest-path tree","level":3,"score":0.3346000015735626},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C147517495","wikidata":"https://www.wikidata.org/wiki/Q5581241","display_name":"Gomory\u2013Hu tree","level":5,"score":0.3228999972343445},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.10626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.10626","pdf_url":"https://arxiv.org/pdf/2509.10626","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2509.10626","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.10626","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"pmh:oai:arXiv.org:2509.10626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.10626","pdf_url":"https://arxiv.org/pdf/2509.10626","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,99,128],"Multimarginal":[1],"Schr\u00f6dinger":[2],"Bridge":[3],"(MSB)":[4],"finds":[5],"the":[6,24,49,53,57,61,73,79,90,114,118,123,126,146],"optimal":[7,54,62,74,115],"coupling":[8,63],"among":[9],"a":[10,19,103,111,132],"collection":[11],"of":[12,51,113,117,125],"random":[13],"vectors":[14],"with":[15,39,106],"known":[16,20],"statistics":[17],"and":[18,47,122],"correlation":[21,28],"structure.":[22],"In":[23,42],"MSB":[25,55,75],"formulation,":[26],"this":[27,43],"structure":[29],"is":[30],"specified":[31],"\\emph{a":[32],"priori}":[33],"as":[34],"an":[35],"undirected":[36],"connected":[37],"graph":[38,67,105],"measure-valued":[40,85],"vertices.":[41,86],"work,":[44],"we":[45,59],"formulate":[46],"solve":[48],"problem":[50,83,92,137],"finding":[52],"in":[56,96],"sense":[58],"seek":[60],"over":[64,84,138],"all":[65],"possible":[66],"structures.":[68],"We":[69,87],"find":[70],"that":[71,89,139],"computing":[72],"amounts":[76],"to":[77,110],"solving":[78],"minimum":[80,134],"spanning":[81,135],"tree":[82,136],"show":[88],"resulting":[91],"can":[93],"be":[94],"solved":[95],"two":[97],"steps.":[98],"first":[100],"step":[101,130],"constructs":[102],"complete":[104,140],"edge":[107],"weight":[108],"equal":[109],"sum":[112],"value":[116],"corresponding":[119],"bimarginal":[120],"SB":[121],"entropies":[124],"endpoints.":[127],"second":[129],"solves":[131],"standard":[133],"weighted":[141],"graph.":[142],"Numerical":[143],"experiments":[144],"illustrate":[145],"proposed":[147],"solution.":[148]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-12T00:00:00"}