{"id":"https://openalex.org/W7159600517","doi":"https://doi.org/10.48550/arxiv.2604.27651","title":"Solving Hypergraph Laplacian Systems in Almost-Linear Time","display_name":"Solving Hypergraph Laplacian Systems in Almost-Linear Time","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159600517","doi":"https://doi.org/10.48550/arxiv.2604.27651"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.27651","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27651","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2604.27651","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134933266","display_name":"Yuichi Yoshida","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yoshida, Yuichi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134933266"],"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":0.7954999804496765,"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":0.7954999804496765,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0348999984562397,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.026100000366568565,"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/hypergraph","display_name":"Hypergraph","score":0.6381000280380249},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6186000108718872},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4851999878883362},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4844000041484833},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.36160001158714294},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.34529998898506165},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.3416999876499176}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7759000062942505},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6381000280380249},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6186000108718872},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4207000136375427},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3580999970436096},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28439998626708984},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.27651","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27651","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.27651","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27651","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"For":[0,32],"a":[1,7,53,57,78,87,105,113,150,163,167],"connected":[2],"weighted":[3],"hypergraph,":[4],"we":[5],"give":[6],"randomized":[8,38,178],"almost-linear-time":[9,179],"solver":[10,176],"for":[11,15,118,182],"the":[12,16,21,27,74,121,125,143,155,174,183],"Poisson":[13,175],"problem":[14,80],"cut-based":[17,185],"hypergraph":[18,186],"Laplacian":[19],"in":[20,41],"natural":[22],"input":[23],"size":[24],"$P=\\sum_{e\\in":[25],"E}|e|$,":[26],"sum":[28],"of":[29,124],"hyperedge":[30,130,139],"sizes.":[31],"every":[33],"fixed":[34],"constant":[35],"$C&gt;0$,":[36],"our":[37],"algorithm":[39],"runs":[40],"$P^{1+o(1)}$":[42],"time":[43],"and,":[44],"with":[45,60],"high":[46],"probability":[47],"over":[48],"its":[49],"internal":[50],"randomness,":[51],"returns":[52],"primal":[54,95,106,119,164],"point":[55],"and":[56,158],"dual":[58,76,89,126],"certificate,":[59],"additive":[61],"optimality":[62],"gap":[63],"at":[64],"most":[65],"$\\exp(-\\log^C":[66],"P)$.":[67],"A":[68],"key":[69],"step":[70],"is":[71,94,112,140],"to":[72,173],"rewrite":[73],"Fenchel":[75],"as":[77],"convex-flow":[79],"on":[81,154],"an":[82],"auxiliary":[83,156],"$O(P)$-arc":[84],"graph,":[85,157],"yielding":[86],"near-optimal":[88],"flow.":[90],"The":[91],"main":[92,109],"difficulty":[93],"recovery,":[96,120],"because":[97],"this":[98],"flow":[99,127],"does":[100],"not":[101],"by":[102],"itself":[103],"determine":[104],"potential.":[107,165],"Our":[108],"new":[110],"ingredient":[111],"recovery":[114],"theorem":[115],"showing":[116],"that,":[117],"detailed":[122],"routing":[123],"inside":[128],"each":[129],"gadget":[131],"can":[132],"be":[133],"discarded:":[134],"one":[135],"nonnegative":[136],"scalar":[137],"per":[138],"enough.":[141],"After":[142],"necessary":[144],"finite-precision":[145],"rounding,":[146],"these":[147],"scalars":[148],"define":[149],"linear-cost":[151],"min-cost-flow":[152],"instance":[153],"solving":[159],"it":[160],"exactly":[161],"recovers":[162],"Finally,":[166],"ground-vertex":[168],"reduction":[169],"from":[170],"regularized":[171],"objectives":[172],"gives":[177],"resolvent/proximal":[180],"primitives":[181],"same":[184],"Laplacian.":[187]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-02T00:00:00"}
