{"id":"https://openalex.org/W2167579893","doi":"https://doi.org/10.1137/s0097539794264585","title":"Low-Degree Spanning Trees of Small Weight","display_name":"Low-Degree Spanning Trees of Small Weight","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W2167579893","doi":"https://doi.org/10.1137/s0097539794264585","mag":"2167579893"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794264585","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794264585","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cs/0205043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Samir Khuller","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samir Khuller","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Balaji Raghavachari","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Balaji Raghavachari","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Neal Young","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neal Young","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0638,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.88009091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"2","first_page":"355","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5449000000953674,"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":0.5449000000953674,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.3637000024318695,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.01810000091791153,"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/spanning-tree","display_name":"Spanning tree","score":0.9075000286102295},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.8830999732017517},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.7541999816894531},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.7211999893188477},{"id":"https://openalex.org/keywords/shortest-path-tree","display_name":"Shortest-path tree","score":0.6748999953269958},{"id":"https://openalex.org/keywords/k-minimum-spanning-tree","display_name":"k-minimum spanning tree","score":0.6444000005722046},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.6237999796867371},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.5541999936103821}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.9075000286102295},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.8830999732017517},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7738000154495239},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.7541999816894531},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7486000061035156},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.7211999893188477},{"id":"https://openalex.org/C23394520","wikidata":"https://www.wikidata.org/wiki/Q4919350","display_name":"Shortest-path tree","level":3,"score":0.6748999953269958},{"id":"https://openalex.org/C202750272","wikidata":"https://www.wikidata.org/wiki/Q6322849","display_name":"k-minimum spanning tree","level":5,"score":0.6444000005722046},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.6237999796867371},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.5541999936103821},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5228000283241272},{"id":"https://openalex.org/C65949645","wikidata":"https://www.wikidata.org/wiki/Q5283163","display_name":"Distributed minimum spanning tree","level":3,"score":0.5185999870300293},{"id":"https://openalex.org/C199346575","wikidata":"https://www.wikidata.org/wiki/Q4925151","display_name":"Reverse-delete algorithm","level":4,"score":0.49779999256134033},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4652000069618225},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.43479999899864197},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3790999948978424},{"id":"https://openalex.org/C1649724","wikidata":"https://www.wikidata.org/wiki/Q470813","display_name":"Prim's algorithm","level":4,"score":0.31769999861717224},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.2879999876022339},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.25920000672340393}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539794264585","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794264585","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/0205043","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0205043","pdf_url":"https://arxiv.org/pdf/cs/0205043","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cs/0205043","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0205043","pdf_url":"https://arxiv.org/pdf/cs/0205043","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1502069391","https://openalex.org/W2001139415","https://openalex.org/W2022563199","https://openalex.org/W2023457294","https://openalex.org/W2024833542","https://openalex.org/W2038858023","https://openalex.org/W2044119054","https://openalex.org/W2055336889","https://openalex.org/W2056839231","https://openalex.org/W2066700938","https://openalex.org/W2088839217","https://openalex.org/W2113947299"],"related_works":[],"abstract_inverted_index":{"Given":[0],"n":[1,53],"points":[2,54,142,159],"in":[3,18,55,134,143,160],"the":[4,6,20,32,56,73,99,127,129,180,189],"plane,":[5,57],"degree-K":[7,37],"spanning-tree":[8],"problem":[9,33],"asks":[10],"for":[11,40,48,150,198],"a":[12,60,76,86,102,118,165,183],"spanning":[13,38,61,78,87,104,120,166,185],"tree":[14,62,88,121,167],"of":[15,22,34,52,63,75,89,101,126,158,168,182],"minimum":[16,77,103,119,184],"weight":[17,67,74,93,100,172,181],"which":[19],"degree":[21,64,90,169],"each":[23],"vertex":[24],"is":[25,45,68,81,94,122,147,173,188],"at":[26,69,95,174],"most":[27,70,96,175],"K.":[28],"This":[29,187],"paper":[30,191],"addresses":[31],"computing":[35],"low-weight":[36],"trees":[39,130],"$K":[41],">":[42],"2$.":[43],"It":[44,80,146],"shown":[46,82,148],"that":[47,83,149,192],"an":[49,155],"arbitrary":[50,156],"collection":[51,157],"there":[58,84],"exists":[59,85],"3":[65,170],"whose":[66,92,171],"1.5":[71],"times":[72,98,179],"tree.":[79,105,186],"4":[91],"1.25":[97],"These":[106],"results":[107,138],"solve":[108],"open":[109],"problems":[110],"posed":[111],"by":[112],"Papadimitriou":[113],"and":[114],"Vazirani.":[115],"Moreover,":[116],"if":[117],"given":[123],"as":[124],"part":[125],"input,":[128],"can":[131],"be":[132],"computed":[133],"$O(n)$":[135],"time.":[136],"The":[137],"are":[139],"generalized":[140],"to":[141],"higher":[144],"dimensions.":[145],"any":[151],"$d":[152],"\\geqslant":[153],"3$,":[154],"$\\Re":[161],"^d":[162],"$":[163],"contains":[164],"${5":[176],"/":[177],"3}$":[178],"first":[190],"achieves":[193],"factors":[194],"better":[195],"than":[196],"2":[197],"these":[199],"problems.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}