{"id":"https://openalex.org/W2024747753","doi":"https://doi.org/10.7155/jgaa.00230","title":"Minmax Tree Cover in the Euclidean Space","display_name":"Minmax Tree Cover in the Euclidean Space","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2024747753","doi":"https://doi.org/10.7155/jgaa.00230","mag":"2024747753"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.00230","pdf_url":null,"source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"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":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.7155/jgaa.00230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066500293","display_name":"Seigo Karakawa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seigo Karakawa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053143888","display_name":"Ehab Morsy","orcid":"https://orcid.org/0000-0002-3489-6736"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ehab Morsy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073738140","display_name":"Hiroshi Nagamochi","orcid":"https://orcid.org/0000-0002-8332-1517"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hiroshi Nagamochi","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.726289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":82,"max":83},"biblio":{"volume":"15","issue":"3","first_page":"345","last_page":"371"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9892,"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":0.9892,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.965,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.939,"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":[],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.84083277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.712214},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6275639},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5118891},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.50184727},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.48962075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4585727},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.4197713},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4164383},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41469052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1510531},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12597358},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.00230","pdf_url":null,"source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"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":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.1280","pdf_url":"http://jgaa.info/accepted/2011/KarakawaMorsyNagamochi2011.15.3.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.00230","pdf_url":null,"source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"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":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2895916002","https://openalex.org/W2474724840","https://openalex.org/W2369683208","https://openalex.org/W2362133437","https://openalex.org/W2084836983","https://openalex.org/W2016058626","https://openalex.org/W1977348009","https://openalex.org/W1814049089","https://openalex.org/W1555347637","https://openalex.org/W1530911128"],"abstract_inverted_index":{"Let":[0],"G\u2009=\u2009(V,E)":[1],"be":[2],"an":[3,194],"edge-weighted":[4],"graph,":[5],"and":[6,97,145,160],"let":[7],"w(H)":[8],"denote":[9],"the":[10,13,16,29,49,53,98,103,107,117,126,135,138,147,177,190],"sum":[11],"of":[12,15,22,45,48,56,72,90,106,121,180],"weights":[14],"edges":[17],"in":[18,39,83,137],"a":[19,25,42,68,80],"subgraph":[20],"H":[21],"G.":[23,73],"Given":[24],"positive":[26],"integer":[27],"k,":[28],"balanced":[30,109],"tree":[31,71,110],"partitioning":[32,92,111,187],"problem":[33,75,136],"requires":[34],"to":[35,59,174],"cover":[36],"all":[37],"vertices":[38],"V":[40],"by":[41],"set":[43],"$\\mathcal{T}$":[44],"k":[46],"trees":[47],"graph":[50,91,186],"so":[51],"that":[52,116,153],"ratio":[54,104],"\u03b1":[55,105,122],"$\\max_{T\\in":[57],"\\mathcal{T}}w(T)$":[58],"w(T":[60],"*)/k":[61],"is":[62,114,123,193],"minimized,":[63],"where":[64],"T":[65],"*":[66],"denotes":[67],"minimum":[69],"spanning":[70],"The":[74],"has":[76],"been":[77],"used":[78],"as":[79],"core":[81],"analysis":[82],"designing":[84],"approximation":[85,183],"algorithms":[86,184],"for":[87,125,158,167,185],"several":[88,181],"types":[89],"problems":[93,188],"over":[94],"metric":[95,128,191],"spaces,":[96],"performance":[99,178],"guarantees":[100,179],"depend":[101],"on":[102,150],"corresponding":[108],"problems.":[112],"It":[113],"known":[115],"best":[118],"possible":[119],"value":[120],"2":[124,149],"general":[127],"space.":[129,196],"In":[130],"this":[131],"paper,":[132],"we":[133],"study":[134],"d-dimensional":[139],"Euclidean":[140,195],"space":[141,192],"\u211d":[142],"d":[143],",":[144],"break":[146],"bound":[148],"\u03b1,":[151],"showing":[152],"$\\alpha":[154,161],"<2\\sqrt{3}-3/2":[155],"\\fallingdotseq":[156,165],"1.964$":[157],"d\u2009\u2265\u20093":[159],"<(13":[162],"+":[163],"\\sqrt{109})/12":[164],"1.953$":[166],"d\u2009=\u20092.":[168],"These":[169],"new":[170],"results":[171],"enable":[172],"us":[173],"directly":[175],"improve":[176],"existing":[182],"if":[189]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2024747753","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-01-18T03:03:00.202049","created_date":"2016-06-24"}