{"id":"https://openalex.org/W2625857725","doi":"https://doi.org/10.1137/15m1034854","title":"Combinatorial Algorithms for Minimizing the Maximum Laplacian and Signless Laplacian Eigenvalues of Weighted Graphs","display_name":"Combinatorial Algorithms for Minimizing the Maximum Laplacian and Signless Laplacian Eigenvalues of Weighted Graphs","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2625857725","doi":"https://doi.org/10.1137/15m1034854","mag":"2625857725"},"language":"en","primary_location":{"id":"doi:10.1137/15m1034854","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1034854","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5058749822","display_name":"Christoph Helmberg","orcid":"https://orcid.org/0000-0002-5288-8000"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christoph Helmberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084454009","display_name":"Israel Rocha","orcid":"https://orcid.org/0000-0003-3590-1872"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Israel Rocha","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023581725","display_name":"Uwe Schwerdtfeger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uwe Schwerdtfeger","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058749822"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05965494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"2","first_page":"1196","last_page":"1216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9901000261306763,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9761999845504761,"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/combinatorics","display_name":"Combinatorics","score":0.7899047136306763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.747443675994873},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6490398645401001},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5733368992805481},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5012996196746826},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5004899501800537},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.49490875005722046},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4004638195037842},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.10525315999984741}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7899047136306763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.747443675994873},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6490398645401001},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5733368992805481},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5012996196746826},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5004899501800537},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.49490875005722046},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4004638195037842},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.10525315999984741},{"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:10.1137/15m1034854","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1034854","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4911882083","display_name":null,"funder_award_id":"PROBRAL 408/13","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G5133193296","display_name":null,"funder_award_id":"PROBRAL 56267227","funder_id":"https://openalex.org/F4320320875","funder_display_name":"Deutscher Akademischer Austauschdienst"}],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1587744656","https://openalex.org/W1999545720","https://openalex.org/W2008512148","https://openalex.org/W2031481696","https://openalex.org/W2050536466","https://openalex.org/W2052015874","https://openalex.org/W2066315387","https://openalex.org/W2068332510","https://openalex.org/W2075551470","https://openalex.org/W2083412275","https://openalex.org/W2087638833","https://openalex.org/W2134711723","https://openalex.org/W2148597446","https://openalex.org/W2161247714","https://openalex.org/W2168986492","https://openalex.org/W4232112990"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W2080136900","https://openalex.org/W2372768926","https://openalex.org/W2999799752","https://openalex.org/W2054458431","https://openalex.org/W154856185","https://openalex.org/W2383428243","https://openalex.org/W58770712"],"abstract_inverted_index":{"We":[0],"provide":[1],"strongly":[2],"polynomial":[3],"time":[4,63],"combinatorial":[5],"algorithms":[6],"to":[7],"minimize":[8],"the":[9,13,21,33,55,66],"largest":[10],"eigenvalue":[11],"of":[12,16,25,48,68],"weighted":[14,22],"Laplacian":[15,24],"a":[17,49],"bipartite":[18],"graph":[19,28,40],"and":[20],"signless":[23],"an":[26],"arbitrary":[27],"by":[29,38],"redistributing":[30],"weights":[31],"among":[32],"edges.":[34],"This":[35],"is":[36],"accomplished":[37],"solving":[39],"embedding":[41],"problems":[42],"which":[43],"arise":[44],"as":[45],"dual":[46],"programs":[47],"semidefinite":[50],"programming":[51],"formulation.":[52],"In":[53],"particular,":[54],"problem":[56],"for":[57],"trees":[58],"can":[59],"be":[60],"solved":[61],"in":[62,65],"cubic":[64],"number":[67],"vertices.":[69]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}