{"id":"https://openalex.org/W2013749552","doi":"https://doi.org/10.1137/110859658","title":"On Minimizing the Spectral Width of Graph Laplacians and Associated Graph Realizations","display_name":"On Minimizing the Spectral Width of Graph Laplacians and Associated Graph Realizations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2013749552","doi":"https://doi.org/10.1137/110859658","mag":"2013749552"},"language":"en","primary_location":{"id":"doi:10.1137/110859658","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110859658","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009854383","display_name":"Frank G\u00f6ring","orcid":"https://orcid.org/0000-0001-8331-2138"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Frank G\u00f6ring","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058749822","display_name":"Christoph Helmberg","orcid":"https://orcid.org/0000-0002-5288-8000"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Helmberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040342822","display_name":"Susanna Rei\u00df","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susanna Reiss","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009854383"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3956743,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67865515,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"23","issue":"2","first_page":"834","last_page":"856"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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":0.9901000261306763,"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/mathematics","display_name":"Mathematics","score":0.8245060443878174},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6830806136131287},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.6649407148361206},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.6205897331237793},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6200196146965027},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5221048593521118},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4823321998119354},{"id":"https://openalex.org/keywords/graph-bandwidth","display_name":"Graph bandwidth","score":0.45443597435951233},{"id":"https://openalex.org/keywords/graph-energy","display_name":"Graph energy","score":0.4320825934410095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40804430842399597},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4014318287372589},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3366253077983856}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8245060443878174},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6830806136131287},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.6649407148361206},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.6205897331237793},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6200196146965027},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5221048593521118},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4823321998119354},{"id":"https://openalex.org/C134727501","wikidata":"https://www.wikidata.org/wiki/Q5597073","display_name":"Graph bandwidth","level":5,"score":0.45443597435951233},{"id":"https://openalex.org/C78913703","wikidata":"https://www.wikidata.org/wiki/Q5597087","display_name":"Graph energy","level":5,"score":0.4320825934410095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40804430842399597},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4014318287372589},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3366253077983856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110859658","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110859658","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W5452359","https://openalex.org/W40462281","https://openalex.org/W126388424","https://openalex.org/W1499675658","https://openalex.org/W1512522810","https://openalex.org/W1530202807","https://openalex.org/W1543336461","https://openalex.org/W1548134571","https://openalex.org/W1580423614","https://openalex.org/W1587744656","https://openalex.org/W1589331344","https://openalex.org/W1965094948","https://openalex.org/W1980352837","https://openalex.org/W1987717935","https://openalex.org/W1988378563","https://openalex.org/W1995658164","https://openalex.org/W2000998728","https://openalex.org/W2002276939","https://openalex.org/W2006096184","https://openalex.org/W2008512148","https://openalex.org/W2029939597","https://openalex.org/W2036074541","https://openalex.org/W2055993677","https://openalex.org/W2073794221","https://openalex.org/W2078289947","https://openalex.org/W2083412275","https://openalex.org/W2084148362","https://openalex.org/W2092812429","https://openalex.org/W2100440346","https://openalex.org/W2105661768","https://openalex.org/W2106508535","https://openalex.org/W2109156232","https://openalex.org/W2114189119","https://openalex.org/W2120204400","https://openalex.org/W2120899029","https://openalex.org/W2127241418","https://openalex.org/W2148597446","https://openalex.org/W2151417892","https://openalex.org/W2157298752","https://openalex.org/W2160548060","https://openalex.org/W2161247714","https://openalex.org/W2168986492","https://openalex.org/W2171567099","https://openalex.org/W2188609405","https://openalex.org/W2552502002","https://openalex.org/W2808908972","https://openalex.org/W2983896310","https://openalex.org/W3105329945","https://openalex.org/W4212845867","https://openalex.org/W4250855070","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1977445720","https://openalex.org/W2165755074","https://openalex.org/W156426934","https://openalex.org/W2391222362","https://openalex.org/W2954396051","https://openalex.org/W2782821035","https://openalex.org/W3123547646","https://openalex.org/W2389330739","https://openalex.org/W2497161677","https://openalex.org/W2105661768"],"abstract_inverted_index":{"Extremal":[0],"eigenvalues":[1,122,140],"and":[2,20,37,43,65,110,114],"eigenvectors":[3,113,137],"of":[4,8,14,28,47,55,57,73,79,86,98,102,107,156,195],"the":[5,12,26,40,44,48,53,58,61,77,88,96,100,108,111,153,157,165,170,176,193,196],"Laplace":[6],"matrix":[7],"a":[9,29,74,129],"graph":[10,18,21,75,109,142,197],"form":[11],"core":[13],"many":[15],"bounds":[16],"on":[17,117],"parameters":[19],"optimization":[22],"problems.":[23],"For":[24],"example,":[25],"value":[27],"uniform":[30],"sparsest":[31],"cut":[32],"is":[33,149],"bounded":[34],"from":[35],"below":[36],"above":[38],"by":[39,52],"second":[41,66,177],"smallest":[42,67,178],"largest":[45],"eigenvalue":[46,68,167,179],"weighted":[49,71],"Laplacian":[50],"divided":[51],"number":[54],"nodes":[56],"graph.":[59,158],"Minimizing":[60],"difference":[62],"between":[63,104],"maximum":[64,166],"over":[69],"edge":[70],"Laplacians":[72],"reduces":[76],"size":[78],"this":[80,84],"interval.":[81],"We":[82],"study":[83],"problem":[85,132],"minimizing":[87],"spectral":[89],"width":[90],"for":[91,175],"its":[92],"own":[93],"sake":[94],"with":[95],"goal":[97],"advancing":[99],"understanding":[101],"connections":[103],"structural":[105],"properties":[106],"corresponding":[112,130,163],"eigenvalues.":[115],"Building":[116],"previous":[118],"work":[119],"where":[120],"these":[121],"were":[123],"investigated":[124],"separately,":[125],"we":[126],"show":[127],"that":[128],"dual":[131],"allows":[133],"us":[134],"to":[135,138,152,164],"view":[136],"optimized":[139],"as":[141],"realizations":[143,162,187],"in":[144,189],"Euclidean":[145],"space,":[146],"whose":[147],"structure":[148,155],"tightly":[150],"linked":[151],"separator":[154],"In":[159],"particular,":[160],"optimal":[161,186],"fold":[168,181],"toward":[169],"barycenter":[171],"along":[172,183],"separators,":[173],"while":[174],"they":[180],"outward":[182],"separators.":[184],"Furthermore,":[185],"exist":[188],"dimension":[190],"at":[191],"most":[192],"tree-width":[194],"plus":[198],"one.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}