{"id":"https://openalex.org/W7138845223","doi":"https://doi.org/10.48550/arxiv.2603.15782","title":"A Fast Approximation Algorithm for the Minimum Balanced Vertex Separator in a Graph","display_name":"A Fast Approximation Algorithm for the Minimum Balanced Vertex Separator in a Graph","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7138845223","doi":"https://doi.org/10.48550/arxiv.2603.15782"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.15782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15782","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":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.2603.15782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130147212","display_name":"Vladimir N Kolmogorov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kolmogorov, Vladimir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130062445","display_name":"Jack Spalding-Jamieson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spalding-Jamieson, Jack","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":0.9314000010490417,"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":0.9314000010490417,"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":0.0421999990940094,"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":0.004900000058114529,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5515999794006348},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5062999725341797},{"id":"https://openalex.org/keywords/separator","display_name":"Separator (oil production)","score":0.4645000100135803},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.45019999146461487},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4171999990940094},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.37310001254081726},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36250001192092896},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.35679998993873596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6107000112533569},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5694000124931335},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5515999794006348},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5062999725341797},{"id":"https://openalex.org/C185004128","wikidata":"https://www.wikidata.org/wiki/Q3011536","display_name":"Separator (oil production)","level":2,"score":0.4645000100135803},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.45019999146461487},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4171999990940094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39579999446868896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3889999985694885},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.33469998836517334},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.2540000081062317},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.15782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15782","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":"doi:10.48550/arxiv.2603.15782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.15782","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":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":{"We":[0],"present":[1],"a":[2,16,19,29,48,58,85,123],"family":[3],"of":[4,42,62,88,128,142,165],"fast":[5],"pseudo-approximation":[6],"algorithms":[7,119],"for":[8,67,73,80,98,112,148],"the":[9,108,129,135,162],"minimum":[10],"balanced":[11],"vertex":[12,40,60,86],"separator":[13,41,61,87],"problem":[14,114],"in":[15,53,94,115],"graph.":[17],"Given":[18],"graph":[20],"$G=(V,E)$":[21],"with":[22],"$n$":[23],"vertices":[24],"and":[25,28,144,156],"$m$":[26],"edges,":[27],"(constant)":[30],"balance":[31],"parameter":[32],"$c\\in(0,1/2)$,":[33],"where":[34],"$G$":[35],"has":[36],"some":[37],"(unknown)":[38],"$c$-balanced":[39],"size":[43,63,89],"${\\rm":[44],"OPT}_c$,":[45],"we":[46,82,132],"give":[47],"(Monte-Carlo":[49],"randomized)":[50],"algorithm":[51,105],"running":[52],"$O(n^{O(\\varepsilon)}m^{1+o(1)})$":[54],"time":[55,95,153,163],"that":[56],"produces":[57],"$\u0398(1)$-balanced":[59],"$O({\\rm":[64,90],"OPT}_c\\cdot\\sqrt{(\\log":[65],"n)/\\varepsilon})$":[66],"any":[68,74],"value":[69],"$\\varepsilon\\in[\u0398(1/\\log(n)),\u0398(1)]$.":[70],"In":[71],"particular,":[72],"function":[75],"$f(n)=\u03c9(1)$":[76],"(including":[77],"$f(n)=\\log\\log":[78],"n$,":[79],"instance),":[81],"can":[83],"produce":[84],"OPT}_c\\cdot\\sqrt{\\log":[91],"n}\\cdot":[92],"f(n))$":[93],"$O(m^{1+o(1)})$.":[96],"Moreover,":[97],"an":[99],"arbitrarily":[100],"small":[101],"constant":[102],"$\\varepsilon=\u0398(1)$,":[103],"our":[104],"also":[106],"achieves":[107],"best-known":[109],"approximation":[110],"ratio":[111],"this":[113],"$O(m^{1+\u0398(\\varepsilon)})$":[116],"time.":[117],"The":[118],"are":[120],"based":[121],"on":[122],"semidefinite":[124],"programming":[125],"(SDP)":[126],"relaxation":[127],"problem,":[130],"which":[131],"solve":[133],"using":[134],"Matrix":[136],"Multiplicative":[137],"Weight":[138],"Update":[139],"(MMWU)":[140],"framework":[141],"Arora":[143],"Kale.":[145],"Our":[146],"oracle":[147],"MMWU":[149],"uses":[150],"$O(n^{O(\\varepsilon)}\\text{polylog}(n))$":[151],"almost-linear":[152],"maximum-flow":[154,166],"computations,":[155],"would":[157],"be":[158],"sped":[159],"up":[160],"if":[161],"complexity":[164],"improves.":[167]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-20T00:00:00"}
