{"id":"https://openalex.org/W4386996886","doi":"https://doi.org/10.3390/e25101376","title":"Iterated Clique Reductions in Vertex Weighted Coloring for Large Sparse Graphs","display_name":"Iterated Clique Reductions in Vertex Weighted Coloring for Large Sparse Graphs","publication_year":2023,"publication_date":"2023-09-24","ids":{"openalex":"https://openalex.org/W4386996886","doi":"https://doi.org/10.3390/e25101376","pmid":"https://pubmed.ncbi.nlm.nih.gov/37895498"},"language":"en","primary_location":{"id":"doi:10.3390/e25101376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101376","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1376/pdf?version=1695548439","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/10/1376/pdf?version=1695548439","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101739242","display_name":"Yi Fan","orcid":"https://orcid.org/0009-0000-5360-5263"},"institutions":[{"id":"https://openalex.org/I4210167317","display_name":"Qiannan Normal College For Nationalities","ror":"https://ror.org/05szpc322","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210167317"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Fan","raw_affiliation_strings":["School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China","institution_ids":["https://openalex.org/I4210167317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029385936","display_name":"Zaijun Zhang","orcid":"https://orcid.org/0000-0002-0690-1673"},"institutions":[{"id":"https://openalex.org/I4210167317","display_name":"Qiannan Normal College For Nationalities","ror":"https://ror.org/05szpc322","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210167317"]},{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zaijun Zhang","raw_affiliation_strings":["Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Province, Duyun 558000, China","School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Province, Duyun 558000, China","institution_ids":["https://openalex.org/I178232147"]},{"raw_affiliation_string":"School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China","institution_ids":["https://openalex.org/I4210167317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101517339","display_name":"Quan Yu","orcid":"https://orcid.org/0000-0002-4486-2070"},"institutions":[{"id":"https://openalex.org/I4210167317","display_name":"Qiannan Normal College For Nationalities","ror":"https://ror.org/05szpc322","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210167317"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quan Yu","raw_affiliation_strings":["School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China","institution_ids":["https://openalex.org/I4210167317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085904657","display_name":"Yongxuan Lai","orcid":"https://orcid.org/0000-0002-2883-0781"},"institutions":[{"id":"https://openalex.org/I181361081","display_name":"Longyan University","ror":"https://ror.org/0483s5p06","country_code":"CN","type":"education","lineage":["https://openalex.org/I181361081"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongxuan Lai","raw_affiliation_strings":["School of Mathematics and Information Engineering, Longyan University, Longyan 364000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Engineering, Longyan University, Longyan 364000, China","institution_ids":["https://openalex.org/I181361081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037325282","display_name":"Kaile Su","orcid":"https://orcid.org/0000-0001-6741-9699"},"institutions":[{"id":"https://openalex.org/I11701301","display_name":"Griffith University","ror":"https://ror.org/02sc3r913","country_code":"AU","type":"education","lineage":["https://openalex.org/I11701301"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Kaile Su","raw_affiliation_strings":["Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD 4111, Australia"],"affiliations":[{"raw_affiliation_string":"Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD 4111, Australia","institution_ids":["https://openalex.org/I11701301"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046212640","display_name":"Yiyuan Wang","orcid":"https://orcid.org/0000-0002-3071-3461"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiyuan Wang","raw_affiliation_strings":["School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077052175","display_name":"Shiwei Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiwei Pan","raw_affiliation_strings":["School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064854962","display_name":"Longin Jan Latecki","orcid":"https://orcid.org/0000-0002-5102-8244"},"institutions":[{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Longin Jan Latecki","raw_affiliation_strings":["Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA","institution_ids":["https://openalex.org/I84392919"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5029385936"],"corresponding_institution_ids":["https://openalex.org/I178232147","https://openalex.org/I4210167317"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19248524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"10","first_page":"1376","last_page":"1376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.749389111995697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6698247790336609},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5971846580505371},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.568784236907959},{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"Vertex connectivity","score":0.5435273051261902},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.4959021508693695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.485000342130661},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4533398449420929},{"id":"https://openalex.org/keywords/clique-problem","display_name":"Clique problem","score":0.42048919200897217},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4125266969203949},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.4119222164154053},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2333255410194397},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.22901514172554016},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.09799221158027649}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.749389111995697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6698247790336609},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5971846580505371},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.568784236907959},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.5435273051261902},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4959021508693695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.485000342130661},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4533398449420929},{"id":"https://openalex.org/C150997102","wikidata":"https://www.wikidata.org/wiki/Q1196873","display_name":"Clique problem","level":5,"score":0.42048919200897217},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4125266969203949},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.4119222164154053},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2333255410194397},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.22901514172554016},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.09799221158027649},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25101376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101376","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1376/pdf?version=1695548439","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:37895498","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37895498","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10606255","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10606255","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10606255/pdf/entropy-25-01376.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:41768175d56843c480151f2f5808f244","is_oa":true,"landing_page_url":"https://doaj.org/article/41768175d56843c480151f2f5808f244","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 10, p 1376 (2023)","raw_type":"article"},{"id":"pmh:oai:research-repository.griffith.edu.au:10072/427748","is_oa":true,"landing_page_url":"http://hdl.handle.net/10072/427748","pdf_url":null,"source":{"id":"https://openalex.org/S4306402548","display_name":"Griffith Research Online (Griffith University, Queensland, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11701301","host_organization_name":"Griffith University","host_organization_lineage":["https://openalex.org/I11701301"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.3390/e25101376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101376","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1376/pdf?version=1695548439","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1592618623","display_name":null,"funder_award_id":"Qiankehe Foundation-ZK[2022] General 550","funder_id":"https://openalex.org/F4320336617","funder_display_name":"Science and Technology Program of Guizhou Province"},{"id":"https://openalex.org/G1904811900","display_name":null,"funder_award_id":"61806050","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336617","display_name":"Science and Technology Program of Guizhou Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386996886.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1971890464","https://openalex.org/W1977846845","https://openalex.org/W2037817070","https://openalex.org/W2070420791","https://openalex.org/W2090980693","https://openalex.org/W2105821629","https://openalex.org/W2526286943","https://openalex.org/W2559490491","https://openalex.org/W2575613133","https://openalex.org/W2618830253","https://openalex.org/W2740329884","https://openalex.org/W2883592941","https://openalex.org/W2941457051","https://openalex.org/W2998575712","https://openalex.org/W4320490877","https://openalex.org/W4321195629","https://openalex.org/W6772483216","https://openalex.org/W6849415225"],"related_works":["https://openalex.org/W3121666834","https://openalex.org/W2951533720","https://openalex.org/W2794565019","https://openalex.org/W2891037262","https://openalex.org/W4300229885","https://openalex.org/W1487885374","https://openalex.org/W2162082186","https://openalex.org/W4285171291","https://openalex.org/W2617596428","https://openalex.org/W4224326468"],"abstract_inverted_index":{"The":[0,54],"Minimum":[1,14],"Vertex":[2,15],"Weighted":[3],"Coloring":[4,16],"(MinVWC)":[5],"problem":[6,18,30,56],"is":[7,20,31,52,82,100,252],"an":[8,101],"important":[9],"generalization":[10],"of":[11,39,49,68,75,91,148,170,215,229,236],"the":[12,28,47,66,73,80,83,89,121,200,226,245,249],"classic":[13],"(MinVC)":[17],"which":[19,223,239],"NP-hard.":[21],"Given":[22],"a":[23,34,61,69,85,108,132,145,221,237],"simple":[24],"undirected":[25],"graph":[26,166,247],"G=(V,E),":[27],"MinVC":[29],"to":[32,71,106,157,199,234],"find":[33,84],"coloring":[35,86],"s.t.":[36],"any":[37],"pair":[38],"adjacent":[40],"vertices":[41],"are":[42,232],"assigned":[43],"different":[44],"colors":[45,50],"and":[46,64,151,165,168,180,211],"number":[48],"used":[51],"minimized.":[53],"MinVWC":[55],"associates":[57],"each":[58],"vertex":[59],"with":[60],"positive":[62],"weight":[63,67,74],"defines":[65],"color":[70],"be":[72,115],"its":[76],"heaviest":[77],"vertices,":[78],"then":[79],"goal":[81],"that":[87,186,225,235],"minimizes":[88],"sum":[90],"weights":[92],"over":[93],"all":[94,241],"colors.":[95],"Among":[96],"various":[97],"approaches,":[98],"reduction":[99,133,227],"effective":[102],"one.":[103],"It":[104,160],"tries":[105],"obtain":[107],"subgraph":[109],"whose":[110],"optimal":[111,118],"solutions":[112],"can":[113],"conveniently":[114],"extended":[116],"into":[117],"ones":[119],"for":[120,193],"whole":[122,246],"graph,":[123],"without":[124],"costly":[125],"branching.":[126],"In":[127],"this":[128],"paper,":[129],"we":[130,207,219],"propose":[131],"algorithm":[134,143,188,231],"based":[135],"on":[136],"maximal":[137,149,242],"clique":[138,163,175],"enumeration.":[139],"More":[140],"specifically":[141],"our":[142,187,216,230],"utilizes":[144],"certain":[146],"proportion":[147],"cliques":[150,243],"obtains":[152],"lower":[153],"bounds":[154],"in":[155,244],"order":[156],"perform":[158],"reductions.":[159,182],"alternates":[161],"between":[162],"sampling":[164],"reductions":[167,179],"consists":[169],"three":[171],"successive":[172],"procedures:":[173],"promising":[174],"reductions,":[176],"better":[177],"bound":[178],"post":[181],"Experimental":[183],"results":[184],"show":[185],"returns":[189],"considerably":[190],"smaller":[191],"subgraphs":[192],"numerous":[194],"large":[195],"benchmark":[196],"graphs,":[197],"compared":[198],"most":[201],"recent":[202],"method":[203],"named":[204],"RedLS.":[205],"Also,":[206],"evaluate":[208],"individual":[209],"impacts":[210],"some":[212],"practical":[213],"properties":[214],"algorithm.":[217],"Furthermore,":[218],"have":[220],"theorem":[222],"indicates":[224],"effects":[228],"equivalent":[233],"counterpart":[238],"enumerates":[240],"if":[248],"run":[250],"time":[251],"sufficiently":[253],"long.":[254]},"counts_by_year":[],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}